Algebra Frazioni algebriche - matematika.itΒ Β· indica per quali valori le seguenti frazioni...
Transcript of Algebra Frazioni algebriche - matematika.itΒ Β· indica per quali valori le seguenti frazioni...
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 1 di 29
indica per quali valori le seguenti frazioni algebriche perdono di significato
1 1π₯π₯ π₯π₯ = 0
2 2π¦π¦3 π¦π¦ = 0
3 5
π₯π₯2π¦π¦3 π₯π₯ = 0 β¨ π¦π¦ = 0
4 3π₯π₯ππππ ππ = 0 β¨ ππ = 0
5 4ππ3ππ ππ = 0
6 2ππππ7π₯π₯9 π₯π₯ = 0
7 11π₯π₯ππππ3π₯π₯π¦π¦2π§π§4 π₯π₯ = 0 β¨ π¦π¦ = 0 β¨ π§π§ = 0
8 3
π₯π₯ β 1 π₯π₯ = 1
9 2π₯π₯π₯π₯ + 1 π₯π₯ = β1
10 ππ3ππ2
ππ2 β 4 ππ = Β±2
11 5ππ2
π¦π¦2 + 4 βπ¦π¦ β β
12 7π₯π₯π₯π₯ + 7 π₯π₯ = β7
Algebra Frazioni algebriche
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13 5π₯π₯π¦π¦π₯π₯π¦π¦ β 1 π₯π₯π¦π¦ = 1
14 π§π§ β 2π§π§ + 2 π§π§ = β2
15 8π₯π₯ β 1π₯π₯ β 8 π₯π₯ = 8
16 5ππ + ππππ + ππ ππ = βππ
17 7ππ
ππ2 + ππ2 ππ = 0 β§ ππ = 0
18 π₯π₯ + π¦π¦π₯π₯ β π¦π¦ π₯π₯ = π¦π¦
19 7
ππ2 β 49ππ2 ππ = Β±7ππ
20 8
π₯π₯3 β 8π¦π¦3 π₯π₯ = 2π¦π¦
21 6ππ
ππ2π₯π₯ β 5πππ₯π₯ + 6π₯π₯ ππ = 2 β¨ ππ = 3 β¨ π₯π₯ = 0
22 π₯π₯2 β 4
π₯π₯2 β 9π₯π₯ + 8 π₯π₯ = 8 β¨ π₯π₯ = 1
23 7π₯π₯2 β 1
π₯π₯2 β 9π₯π₯ + 14 π₯π₯ = 2 β¨ π₯π₯ = 7
24 π₯π₯ + 2
ππ2 β 2πππ₯π₯ + π₯π₯2 ππ = 1
Algebra Frazioni algebriche
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25 π₯π₯2 + 3π₯π₯2 β 9 π₯π₯ = Β±3
26 ππ3 + 8ππ + 8 ππ = β8
27 ππ(ππ + 7)
ππ2 β 6ππ β 7 ππ = β1 β¨ ππ = 7
indica per quali valori le seguenti frazioni algebriche si annullano allβinterno del C.E.
28 2
4π₯π₯ + 10 β π₯π₯ β β
29 3π₯π₯9π¦π¦ π₯π₯ = 0 ππππππ π¦π¦ β 0
30 11ππ
7ππ + 11 ππ = 0
31 11
11ππ β 7 βππ β β
32 2π₯π₯ β 4
10π₯π₯ β 12 π₯π₯ = 2
33 3ππ + 3ππ β 3ππ
12 ππ + ππ β ππ = 0
34 5ππ + ππππ
5ππ ππ = 0 β¨ ππ = β5
35 ππ + ππππ2 + ππ2 ππ = βππ ππππππ ππ β 0
36 3ππ
ππ2 + 9ππ ππ = 0 ππππππππππ ππππ π π πππ π πππππ π πππππππ π ππ
Algebra Frazioni algebriche
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37 3π₯π₯
12ππ β 3π₯π₯ π₯π₯ = 0 ππππππ ππ β 0
38 5π₯π₯
15ππ β 20ππ π₯π₯ = 0
39 π₯π₯2 β 9 3π₯π₯ β 9
π₯π₯ = β3
π₯π₯ β 3 ππππππππππ ππππ π π πππ π πππππ π πππππππ π ππ
40 ππ2 + 1ππ2 β 1 βππ β β
41 π₯π₯3 β 1π₯π₯2 + 1 π₯π₯ = 1
determina le condizioni di esistenza delle seguenti frazioni algebriche considerando verificate le condizioni di esistenza
42 (ππ2 + 17)3
11ππ ππ β 0
43 3ππ
2ππ + 8 ππ β β4
44 2π₯π₯2
2π₯π₯ + 3 π₯π₯ β β32
45 2ππ + ππππ + 2ππ ππ β β2ππ
46 1
(ππ β 1)(ππ + 5) ππ β 1 β§ ππ β β5
47 3π₯π₯ + 5π₯π₯2 β 9 π₯π₯ β β3 β§ π₯π₯ β 3
48 3π₯π₯
π₯π₯2 + 1 βπ₯π₯ β β
Algebra Frazioni algebriche
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49 ππ β 5
ππ5 β 27ππ2 ππ β 0 β§ ππ β 3
50 3
ππ2 + ππ ππ β 0 β§ ππ β β1
51 ππ
πππ₯π₯ + 3π₯π₯ π₯π₯ β 0 β§ ππ β β3
52 3ππ + ππ
2ππ3 β 32ππ ππ β 0 β§ ππ β β4 β§ ππ β 4
53 3ππ + 1ππ4 β 256 ππ β β4 β§ ππ β 4
54 π₯π₯ β 1
π₯π₯2 β 6π₯π₯ + 9 π₯π₯ β 3
55 7π₯π₯ β 1
π₯π₯3 + 7π₯π₯2 β π₯π₯ β 7 π₯π₯ β 1 β§ π₯π₯ β β1 β§ π₯π₯ β β7
56 ππ + 2
(ππ2 β 9)(ππ3 β ππ2) ππ β β3 β§ ππ β 3 β§ ππ β 0 β§ ππ β 1
57 11
(ππ β 1)3 ππ β 1
58 13ππ β ππππ4 β ππ4 ππ β ππ β§ ππ β βππ
59 π₯π₯2π¦π¦ + 1π₯π₯2 β 4π¦π¦2 π₯π₯ β β2π¦π¦ β§ π₯π₯ β 2π¦π¦
60 2ππ2 + 8ππ
(ππ + 7)(3π₯π₯ β 2) ππ β β7 β§ π₯π₯ β 23
Algebra Frazioni algebriche
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61 π₯π₯ + 3βπ₯π₯2 β 4 βπ₯π₯ β β
semplificazioni di frazioni algebriche considerando verificate le condizioni di esistenza
62 3π₯π₯
9π₯π₯2 1
3π₯π₯
63 8ππ3ππ
10ππ4ππ4 4ππ
5ππππ3
64 7π₯π₯
14π₯π₯π¦π¦ β 21π₯π₯ 12π¦π¦ β 3
65 5ππ3 β 10ππ2
5ππ3 ππ β 2ππ
66 7ππ4ππ5
21ππ3ππ 13ππππ4
67 ππ2 β 4ππ + 4
3ππ2 β 12 ππ β 2
3(ππ + 2)
68 6π₯π₯π¦π¦ + 3π¦π¦2
8π₯π₯π¦π¦ + 4π¦π¦2 34
69 π₯π₯2 + 2π₯π₯π¦π¦π₯π₯π¦π¦ + 2π¦π¦2
π₯π₯π¦π¦
70 ππ2ππ2 + πππππ₯π₯
ππ2ππ2 ππππ + π₯π₯ππππ
71 3π₯π₯ β 3π¦π¦π¦π¦ β π₯π₯ β3
72 π₯π₯3 + 3π₯π₯2
π₯π₯ + 3 π₯π₯2
Algebra Frazioni algebriche
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73 π₯π₯2 + 5π₯π₯
5π₯π₯ π₯π₯ + 5
5
74 ππ2 β 3ππ9 β 3ππ β
ππ3
75 πππ₯π₯ + πππ₯π₯ β πππ¦π¦ β πππ¦π¦πππ¦π¦ + πππ¦π¦ + πππ₯π₯ + πππ₯π₯
π₯π₯ β π¦π¦π₯π₯ + π¦π¦
76 9πππ¦π¦ β 6πππ₯π₯ β 3πππ₯π₯ + 18πππ¦π¦
3ππ + 6ππ 3π¦π¦ β π₯π₯
77 6ππ2 β 12ππ + 6
ππ2 β 1 6(ππ β 1)ππ + 1
78 ππ3 β ππ3
ππ3ππ3 ππππππ π π πππππππ π πππ π πππππππππππ π ππ
79 2π₯π₯2 β 8
π₯π₯3 β π₯π₯2 β 4π₯π₯ + 4 2
π₯π₯ β 1
80 1 β ππ2
ππ + ππ β ππ2 β ππππ 1 + ππππ + ππ
81 π₯π₯3 β πππ₯π₯2
π₯π₯4 β 2πππ₯π₯3 + ππ2π₯π₯2 1
π₯π₯ β ππ
82 4 β 9ππ2
4 β 6ππ + 2ππ2β3ππ3 3ππ + 2ππ2 + 2
83 ππ2 β 4ππ + 4ππ2 β 4
ππ + 2ππ β 2
84 3π π 2 β 36π π 2 β 6
12
Algebra Frazioni algebriche
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85 3π₯π₯ + 3π¦π¦
4π₯π₯ + 4π¦π¦ + πππ¦π¦ + πππ₯π₯ 34 + ππ
86 π₯π₯2 β 5π₯π₯ + 6π₯π₯2 β 9
π₯π₯ β 2π₯π₯ + 3
87 π₯π₯2 β 5π₯π₯ + 6
3π₯π₯ β 9 π₯π₯ β 2
3
88 16π₯π₯3 + 8π₯π₯
4π₯π₯2 + 1 ππππππ π π πππππππ π πππ π πππππππππππ π ππ
89 4ππ β 4ππ + (ππ β ππ)2
(ππ β ππ)2 4 + ππ β ππππ β ππ
90 π₯π₯4 β 1π₯π₯3 β 1
(π₯π₯ + 1)(π₯π₯2 + 1)π₯π₯2 + π₯π₯ + 1
91 πππ₯π₯ + 2π₯π₯ β ππ β 2πππ₯π₯ β 2π₯π₯ β ππ + 2
ππ + 2ππ β 2
92 ππ3 + 4ππ2 + 4ππ
4 β ππ2 ππ(ππ + 2)
2 β ππ
93 ππ2ππ β 4ππβ2ππ β ππππ 2 β ππ
94 π₯π₯3 β π¦π¦3
3π₯π₯ β 3π¦π¦ π₯π₯2 + π₯π₯π¦π¦ + π¦π¦2
3
95 (ππ β 2)2 + 2ππ
2(ππ3 + 8) 1
2(ππ + 2)
96 π₯π₯2 β 4
π₯π₯2 β 4π₯π₯ + 4 π₯π₯ + 2π₯π₯ β 2
Algebra Frazioni algebriche
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97 ππ2 β 2ππ β 3ππ2 β 6ππ + 9
ππ + 1ππ β 3
98 2ππππ β ππ2 β ππ2
ππ3 β ππ2ππ ππ β ππππ2
99 π₯π₯3π¦π¦3 β π₯π₯π¦π¦
π₯π₯2π¦π¦2 + 1 + 2π₯π₯π¦π¦ π₯π₯π¦π¦(π₯π₯π¦π¦ β 1)π₯π₯π¦π¦ + 1
100 4ππ2 β 4ππππ + ππ2 β 1
4ππ2 + ππ2 + 1 β 4ππππ + 4ππ β 2ππ 2ππ β ππ β 12ππ β ππ + 1
101 π₯π₯3 β π¦π¦3
π₯π₯2 β 2π₯π₯π¦π¦ + π¦π¦2 π₯π₯2 + π₯π₯π¦π¦ + π¦π¦2
π₯π₯ β π¦π¦
102 π₯π₯3 β π¦π¦3
π₯π₯2 β π¦π¦2 π₯π₯2 + π₯π₯π¦π¦ + π¦π¦2
π₯π₯ + π¦π¦
103 ππ3 β 2ππ2 + ππ
ππ3 β 3ππ2 + 3ππ β 1 ππ
ππ β 1
104 π₯π₯2 β 3π₯π₯ + 2π₯π₯2 β π₯π₯ β 2
π₯π₯ β 1π₯π₯ + 1
105 ππ2 + 10ππππ + 25ππ2
ππ4 + 10ππ3ππ + 25ππ2ππ2 1ππ2
106 π₯π₯5 β 16π₯π₯π₯π₯3 β 4π₯π₯ π₯π₯2 + 4
107 2ππ2 + ππ β 10
(ππ2 β 4)(2ππ2 + 5ππ) 1
ππ(ππ + 2)
108 2ππ3 + 2
ππ3 + ππ2 + ππ + 1 2(ππ2 β ππ + 1)
ππ2 + 1
Algebra Frazioni algebriche
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109 8π₯π₯2 β 8
4πππ₯π₯ + 12π₯π₯ + 4ππ + 12 2(π₯π₯ β 1)ππ + 3
110 π₯π₯2 + π¦π¦2 β 2π₯π₯π¦π¦ β π§π§2
3π₯π₯2 β 3π₯π₯π¦π¦ β 3π₯π₯π§π§ π₯π₯ β π¦π¦ + π§π§
3π₯π₯
111 2ππ2 + 2ππ β 12ππ3 β 7ππ + 6
2ππ β 1
112 π₯π₯3 β 3π₯π₯2 + 4π₯π₯2 β π₯π₯ β 2 π₯π₯ β 2
113 2π₯π₯5 + 6π₯π₯4 β 36π₯π₯3
2πππ₯π₯3 β π₯π₯3 β 18πππ₯π₯ + 9π₯π₯ 2π₯π₯2(π₯π₯ + 6)
(2ππ β 1)(π₯π₯ + 3)
114 ππ2 + 2ππ + 1 β ππ2
ππ2 + ππππ + ππ ππ + 1 β ππ
ππ
115 4ππ2 β 25ππ2
50ππ2 β 8ππ2 β12
116 9ππ2 + 25ππ2 β 30 ππππ
9ππ β 15ππ 3ππ β 5ππ
3
117 π₯π₯4 + 1 β 2π₯π₯2
2π₯π₯ + 1+π₯π₯2 (π₯π₯ β 1)2
118 π₯π₯3 β π₯π₯π¦π¦4
3π₯π₯2 β 3π₯π₯π¦π¦2 π₯π₯ + π¦π¦2
3
119 3ππππ+2ππππ+1
2ππππππ 3ππ2ππππ
2
120 4π₯π₯2ππ β 12π₯π₯ππ + 9
4π₯π₯2ππ β 9 2π₯π₯ππ β 32π₯π₯ππ + 3
Algebra Frazioni algebriche
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121 ππ2ππ β ππ2ππ
ππ2ππ + 2ππππππππ + ππ2ππ ππππ β ππππ
ππππ + ππππ
122 2π₯π₯ππ+1 + π₯π₯ππ+2 + π₯π₯ππ
π₯π₯2 β 1 π₯π₯ππ(π₯π₯ + 1)π₯π₯ β 1
123 24π₯π₯2ππ β 24
8π₯π₯4ππ β 8 3
π₯π₯2ππ + 1
esegui le seguenti somme di frazioni algebriche considerando verificate le condizioni di esistenza
124 3 +1π₯π₯
3π₯π₯ + 1π₯π₯
125 πππ₯π₯ β
ππ2π¦π¦ 2πππ¦π¦ β πππ₯π₯
2π₯π₯π¦π¦
126 2ππ β 3π₯π₯
2 β 3πππ₯π₯ππ
127 π₯π₯ + 1 +1
π₯π₯ β 1 π₯π₯2
π₯π₯ β 1
128 1
6π₯π₯ β2
3π₯π₯ +1
2π₯π₯ 0
129 1
2π₯π₯ β5
3π₯π₯ +3
5π₯π₯ β1730x
130 π₯π₯ β1
2π₯π₯ +3π₯π₯2 2x3 β x + 6
2x2
131 π¦π¦
3π₯π₯2 β5
2π₯π₯π¦π¦ +1
6π₯π₯ xy + 2y2 β 15x6x2y
132 2π₯π₯2 + 1π₯π₯2 β
π₯π₯ + 2π₯π₯ + 3
4x2 β 2x + 1x2
Algebra Frazioni algebriche
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133 3
2ππππ +ππ
6ππ2 βππ
9ππ2 27ππππ + 3ππ3 β 2ππ3
18ππ2ππ2
134 3 +1ππ β
ππ2 + ππ + 1ππ + 1
βππ3 + 2ππ2 + 3ππ + 1ππ(ππ + 1)
135 ππ + 1ππ β
11 β ππ
βππ2 β ππ + 1ππ(1 β ππ)
136 ππ + 2ππ2 β 9 +
3ππ
4ππ2 + 2ππ β 27ππ(ππ2 β 9)
137 2 β π¦π¦π₯π₯ β π¦π¦ β
1π¦π¦ 3π¦π¦ β π¦π¦2 β π₯π₯
π¦π¦(π₯π₯ β π¦π¦)
138 2π₯π₯ β 3π¦π¦π₯π₯ β π¦π¦ β
2π₯π₯ β 3π¦π¦π₯π₯ β π¦π¦ 0
139 2π₯π₯2π¦π¦ +
3π¦π¦π₯π₯π¦π¦2 β 1 2 + 3x β x2y
x2y
140 ππ + 2ππ
2ππ +ππ β ππ
3ππ βππ + 4ππ
6ππ 23
141 2π₯π₯ β π¦π¦
3 βπ₯π₯ β 2π¦π¦
4 5x + 2y
12
142 1 β3π₯π₯ β 2π¦π¦5π₯π₯ + 3π¦π¦
2x + 5y5x + 3y
143 1 +π₯π₯π¦π¦ β 2
3π₯π₯π¦π¦ β2π₯π₯π¦π¦
4xy β 83xy
144 11
2ππ2ππ2 β 1 β3
4ππ2ππ2 19 β 4a2b2
4a2b2
Algebra Frazioni algebriche
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145 π₯π₯ + π¦π¦
2π₯π₯ β2π₯π₯ β π¦π¦
3π¦π¦ β3π¦π¦ β π₯π₯
6π₯π₯ 3y β 2x
3y
146 (π₯π₯ β π¦π¦)(π₯π₯ + π¦π¦)
π₯π₯π¦π¦ +2π¦π¦π₯π₯ + 2 β
(π₯π₯ + π¦π¦)2
π₯π₯π¦π¦ 0
147 β3 βππ β 1
9 β 9ππ2 +2
3(ππ + 1) β27a + 209(a + 1)
148 5π₯π₯2 β π₯π₯π¦π¦π₯π₯2 β π¦π¦2 β
3π₯π₯π¦π¦ + π₯π₯ +
2π₯π₯π¦π¦ β π₯π₯ 0
149 (ππ β ππ)(ππ2 + ππππ + ππ2)
2ππ2ππ β3ππ2 + 4ππ2
6ππ2 +16 β
a + b2b
150 1
π₯π₯ β 2 β2
π₯π₯ + 3 β5
π₯π₯2 + π₯π₯ β 6 β1
x + 3
151 π₯π₯ β π¦π¦π₯π₯ + π¦π¦ β
1 β π¦π¦2
π₯π₯2 + π¦π¦2 + 2π₯π₯π¦π¦ x2 β 1
(x + y)2
152 π₯π₯ β 1π₯π₯2 β π¦π¦2 β
π¦π¦ β 1π₯π₯π¦π¦ β π¦π¦2 π₯π₯ β π¦π¦2
π¦π¦(π₯π₯2 β π¦π¦2)
153 ππ
ππ + 2 βππ β 3ππ2 β 4 ππ2 β 3ππ + 3
ππ2 β 4
154 2π₯π₯ + 3π¦π¦π₯π₯ β π¦π¦ +
π₯π₯ + 2π¦π¦π¦π¦ β π₯π₯
π₯π₯ + π¦π¦π₯π₯ β π¦π¦
155 2π₯π₯ β 3π¦π¦π₯π₯ β π¦π¦ β
2π₯π₯ β 3π¦π¦π¦π¦ β π₯π₯
4π₯π₯ β 6π¦π¦π₯π₯ β π¦π¦
156 2π₯π₯ β 3π¦π¦π₯π₯ β π¦π¦ β
2π₯π₯ β 3π¦π¦π₯π₯ + π¦π¦ 4π₯π₯π¦π¦ β 6π¦π¦2
π₯π₯2 β π¦π¦2
Algebra Frazioni algebriche
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157 2ππ + 3ππππ + 2ππ +
2ππ β 3ππππ + 2ππ
4ππππ + 2ππ
158 1
ππ + 1 +1
ππ β 1 β1ππ
ππ2 + 1ππ(ππ2 β 1)
158 ππ +1
ππ β 1 +1
1 β ππ ππ
160 1
ππ2 β 3ππ + 2 +1
ππ β 2 β1
1 βππ 2
ππ β 2
161 ππ +1
ππ β 1 β1
1 β ππ ππ2 β ππ + 2ππ β 1
162 5ππ β 2ππ β
5ππ5ππ + 2 β 1
15ππ2 β 2ππ β 4ππ(5ππ + 2)
163 2ππβ ππππ β ππ +
ππ β 3ππ2ππ β ππ β
ππ2
2ππ2 β 3ππππ + ππ2 ππ + ππ
2ππ β ππ
164 2π₯π₯π₯π₯ + 3 β
3π₯π₯2π₯π₯ + 4 β
1π₯π₯2 + 5π₯π₯ + 6
x2 β x β 22(x2 + 5x + 6)
165 βπππ₯π₯ + πππ¦π¦πππ₯π₯2 β πππ¦π¦2 +
πππππ₯π₯ β πππ¦π¦ b2 β a2
ab(x β y)
166 ππ β 1ππ β 4 β
ππ + 2ππ β 3 β
3ππ2 β 7ππ + 12
23 β a
167 ππ β 4
ππ2 + 9 β 6ππ βππ + 3
ππ2 + ππ β 12 β7
(a β 3)2(a + 4)
168 3ππππ β ππ β
3(ππ + ππ)2
ππ2 β ππππ β3ππππ
9bb β a
169 ππ
3ππ β 3ππ +ππ
2ππ β 2ππ +ππ + 4ππ
6ππ β 6ππ 16
Algebra Frazioni algebriche
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170 4π₯π₯2 + 4π₯π₯ + 1
4π₯π₯ β 8π₯π₯2 β4π₯π₯2 + 1
4π₯π₯ + π₯π₯ 2x + 32 β 4x
171 π₯π₯2
π₯π₯π¦π¦ β π¦π¦2 βπ₯π₯2 + π¦π¦2
π₯π₯2 β π¦π¦2 βπ¦π¦2
π₯π₯π¦π¦ + π¦π¦2 xy
172 π₯π₯ + 1π₯π₯π¦π¦2 β
π₯π₯ β 1π₯π₯2π¦π¦ +
π₯π₯2π¦π¦ β π₯π₯3 + π₯π₯ + π¦π¦π₯π₯3π¦π¦2 β π₯π₯2π¦π¦2
2xy(x β 1)
173 π₯π₯ + 2π₯π₯2 + π₯π₯ +
π₯π₯ + 1βπ₯π₯2 β 2π₯π₯ β 1 β
1π₯π₯
1 β xx(x + 1)
174 ββππ2
3ππππ β 9ππ2 +3ππ
ππ + 3ππ +ππ2 + 9ππ2
ππ2 β 9ππ2 b(b + 3a)
3a(b β 3a)
175 2 + ππππ + 3 β
3ππ β 1ππ2 + ππ β 6 β
ππππ + 3
12 β a
176 π₯π₯2 + 2π₯π₯ + 1π₯π₯2 β 2π₯π₯ + 1 +
π₯π₯ β 11 + π₯π₯ β
2π₯π₯3 + 6π₯π₯3 β π₯π₯2 β π₯π₯ + 1
6x2 β 1
177 2ππ + 4ππ β 9 β
3ππ2 + 13ππ β 8ππ2 β 2ππ β 63 +
2ππ β 5ππ + 7
a β 9a + 7
178 1
π₯π₯ + 5 βπ₯π₯2 β 5π₯π₯π₯π₯3 + 125 β
5 β π₯π₯π₯π₯2 β 5π₯π₯ + 25
x2
x3 + 125
179 ππ β 2ππππ + ππ β
ππ + 2ππππ β ππ +
3ππππππ2 β ππ2 β
3aba2 β b2
180 ππ + 2
ππ2 + ππ β 2 β1
ππ β 1 +ππ
ππ + 2 a
a + 2
181 π₯π₯
π₯π₯2 β 3π₯π₯ + 2 βπ₯π₯2 β π₯π₯π₯π₯ β 2 + 2π₯π₯
x(x β 2)x β 1
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 16 di 29
182 π₯π₯ + 1π₯π₯2 β π₯π₯π¦π¦ β
π¦π¦ β 2π₯π₯π¦π¦ β π¦π¦2 β
3π₯π₯ β π¦π¦
3xy β y β 2xxy(y β x)
183 1
(π₯π₯ β 3)(π₯π₯ β 1) β1
π₯π₯ β 3 +2
π₯π₯2 β 2π₯π₯ β 3 βx
x2 β 1
184 1
(ππ β ππ)(ππ β π₯π₯) +1
(ππ β ππ)(ππ β π₯π₯) +1
(π₯π₯ β ππ)(π₯π₯ β ππ) 0
185 ππ2
ππ2 β ππ2 +ππ2
ππ2 β ππ2 βππππ β ππ2
2ππππ β ππ2 β ππ2 a
a β b
186 1
π₯π₯2 β 2π₯π₯ + 1 + π₯π₯2 + 2π₯π₯ + 1 +2π₯π₯2(π₯π₯ β 1)
π₯π₯3 β 3π₯π₯2 + 3π₯π₯ β 1 x4 + 2
(x β 1)2
187 2
π₯π₯ + 2 +1
βπ₯π₯ β 2 +9π₯π₯2 β 3π₯π₯
3π₯π₯2 + 5π₯π₯ β 2 3x + 1x + 2
188 π₯π₯
π₯π₯ + 1 +π₯π₯2 β π₯π₯π¦π¦ + 2π₯π₯π₯π₯π¦π¦ β π₯π₯ + π¦π¦ β 1 β
π¦π¦1 β π¦π¦
x + yy β 1
189 π₯π₯ β 1
(π₯π₯ β 2)2 β (π₯π₯ β 3)2 +3π₯π₯ β 62π₯π₯ β 5 β
6π₯π₯ β 1525 + 4π₯π₯2 β 20π₯π₯ 2
190 β1π₯π₯ +
π₯π₯2 + 2π¦π¦2
π₯π₯3 + π¦π¦3 +π₯π₯ + 2π¦π¦
π₯π₯2 + π¦π¦2 β π₯π₯π¦π¦ +π¦π¦2 β 4π₯π₯π¦π¦
π₯π₯3 + π₯π₯π¦π¦2 β π₯π₯2π¦π¦ 1
x + y
191 3
ππππ β 2 +2ππππ
5an β 4a2n β 2an
192 π₯π₯2ππ
π₯π₯2ππ + π¦π¦2ππ +12 +
π¦π¦2ππ
π¦π¦2ππ + π₯π₯2ππ 32
193 1
1 + ππππ +1
1 β ππππ β2ππππ
1 β ππ2ππ 2
1 + an
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 17 di 29
194 ππ
π₯π₯ππ + 1 βππ
π₯π₯ππ β 1 +πππ₯π₯ππ β πππ₯π₯ππ
π₯π₯2ππ β 1 a + b
1 β x2n
195 ππππ + 2ππ2ππ + ππππ +
ππππ + 1βππ2ππ β 2ππππ β 1 β
1ππππ
1 β an
an(1 + an)
esegui le moltiplicazioni e divisioni di frazioni algebriche considerando verificate le condizioni di esistenza
196 ππππ7ππ β
ππππ2
ππ7ππ
197 3 βππππ6ππ
ππππ2ππ
198 6
10x3y2 β5x2y
3 1xy
199 β27b3y2
3 β2y
45a2x2 β3ax2by β
3b2y2
5ax
200 a2 β b2
a2 + b2 βa4 β b4
a + b (a + b)(a β b)2
201 4y2
y2 β x2 βx + y
2y 2y
y β x
202 a2 + a + 1
b2 β3b3 β 3ab3
1 β a3 3b
203 x3 β 88 + x3 β
x + 24 + 2x + x2
x β 24 β 2x + x2
204 x2 β 2x β 3
x2 + 2x β 15 βx2 β 4x + 4
x + 2 βx2 + 7x + 10
x2 β x β 2 x β 2
205 2a
1 β 4a2 β4a2 + 4a + 1
2a β 6 a(1 + 2a)
(1 β 2a)(a β 3)
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 18 di 29
206 x2 β 1
x βx + 2
x βx2
x2 + 3x + 2 x β 1
207 a2 + aa + 3 β
a2 + 6a + 92a + 6 β
1a2 + a
12
208 x2 + y2 β xy
x2y2 βx3y2
x3 + y3 x
x + y
209 a2 + 2ab + b2
b2 βb3
a3 + 3a2b + 3ab2 + b3 b
a + b
210 4(x + 3) + x β 3x2(x β 3)(x + 3) β
β9x2 + x4
25x2 β 81 1
5x β 9
211 10a2 β 10b2
x2 β xy βx2 β 2xy + y2
2a2 β 4ab + 2b2 5(a + b)(xβ y)
x(a β b)
212 (7anbn+2) β3
14an+1b2 β οΏ½β6bn
a οΏ½ β9b2n
a2
213 5x β 5y
3xy βΆx2
x β y 5(x β y)2
3x3y
214 x0
y0 βΆxy
yx
215 10a3b3 βΆ οΏ½β5b4
a3 οΏ½ β2a6
b
216 ππ2 β ππππ + 1 β
4ππ + 4ππ2 β 1
4ππππ + 1
217 (π₯π₯ + 1) βπ₯π₯ β 1
3π₯π₯2 + 2π₯π₯ β 1 π₯π₯ β 1
3π₯π₯ β 1
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 19 di 29
218 ππ2 β 92ππ β 4 β
ππ2 β 43ππ + 9
(ππ + 2)(ππ β 3)6
219 ππ2 + πππππ₯π₯2 β π₯π₯π¦π¦ β
π₯π₯2 β π¦π¦2
ππ2 β ππ2 βπππ₯π₯ β π₯π₯ππ5π₯π₯ + 5π¦π¦
ππ5
220 2a2 + 4ab + 2b2
3a2b βΆ4b2 β 4a2
9ab2 3b(a + b)2a(b β a)
221 4a3b2
15xy βΆ οΏ½16a4b4
35x3b2 βΆ8a2b2
49xy οΏ½ 2xab2
21y2
222 2x β 3yx2 β y2 βΆ οΏ½
9y2 + 4x2 β 12xyx3 + xy2 β 2x2y βΆ
2x2 β 3xyx3 β x2y οΏ½
1x + y
223 3y
y β 5 βΆ οΏ½y β 1
2y β 10 βΆ6y
y2 β 1οΏ½ 36y2
(y β 1)2(y + 1)
224 x3 β xy2
x2 + 2xy + y2 βΆ οΏ½x2 β 2xy + y2
x2y β y3 βΆ xyοΏ½ x2y2
225 4x2y3
5x β 5 βΆ οΏ½8x5y3
10xβ 10 βΆy
x4οΏ½ y
x7
226 2a3
a + b βΆ οΏ½4ab
a2 + 2ab + b2 βΆa2 β b2
ab β b2οΏ½ a2(a + b)2
2b2
227 4(x + 2) β 5 β 5x
(x + 1)(x + 2) βΆβx + 3
x2 + 3x + 2 1
228 οΏ½οΏ½y2 β x2
x2y2 οΏ½ βΆ οΏ½y β x
xy οΏ½οΏ½ βΆx + y
xy 1
229 a2 β 3aa2 β 1 βΆ
9a + 3a(aβ 1)β 2a(a + 1)3(a β 1)(a + 1)
3(a β 3)a + 4
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 20 di 29
230 βx2 + y
xy βΆ2xy β (y + 2xy β x2)
2xy βΆ οΏ½β1xοΏ½ 2x
231 β(x β 3y) + x + y
x + y βΆβ3(xβ y) + 3x + y
x β y x β yx + y
232 2a β 3ba2 β b2 βΆ
4a2 β 6ab3a β 3b β
a2 + ab3
12
233 x3 + y3
x2 β y2 βΆx2 β xy + y2
x2 β 2xy + y2 βx β y
3x (x β y)2
3x
234 2x3
x + y βx2 + 2xy + y2
4xy β οΏ½β2y
y2 β x2οΏ½ x2
x β y
235 οΏ½a β1bοΏ½ β οΏ½a +
1bοΏ½ β οΏ½
b2
a2b2 + 2ab + 1οΏ½ ab β 1ab + 1
236 x4 β y4
x3 + x2 βx
x3 + xy2 β y2 β x2 β1 β x2
y β x x + y
x
237 οΏ½1 β4a2οΏ½ β οΏ½
aa + 1 +
4a2 β a β 2οΏ½ βΆ
a3 β a4 + 8 β 8a2 β 2a
2a2(a + 1)
238 b
b2 β a2 β(b β a) βΆ οΏ½οΏ½
b β ab οΏ½ β οΏ½
abb2 β a2οΏ½οΏ½
ba
239 2x β
(x + y)(xβ y) + 2y2
2y(xβ y) βΆx2 + y2
xy β y2 1x
240 y + 1y β 1 β
y2 + y β 2y2 + y βΆ (y2 β 4)
1y(y β 2)
241 4(b β 1) β (3b β 5)
b2 β 4b + 3 βb3 + 3b β 4b2
b2 + 3b βΆ (b + 3) b + 1
(b + 3)2
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 21 di 29
242 οΏ½x2 β 6x + 9
3x β6x
x β 3οΏ½ βx β 2
x2 β x β 6 βΆ(x + 2)
2x β 4(x + 2)2
243 a + a3 β a(a2 β 1)(a2 β 1)(1 + a2) β
a3 β a2 + a β 13a + 1 βΆ
6a
a2
3(a + 1)(3a + 1)
244 ab β a(a + b)
a + b βab β b(a + b)
a + b βa2 + 2ab + b2
ab βΆ ab 1
245 (y4 β 2y3) οΏ½1 +2y +
4y2οΏ½ βΆ y y3 β 8
246 οΏ½a +4a + 4οΏ½ β οΏ½2a β
a2 + aa + 2 οΏ½ β
1a + 3 βΆ
(a + 2)2 1
a + 2
247 2x οΏ½1 βx β 1
2x β2y
x + yοΏ½(x + y) x2 + x + y β 3xy
248 1 + x + 2x2 β x(1 + x)
x(1β x)(1 + x) βx2 + 1 + 2x
x2 + 1 βx
x + 1 βΆ1
1 β x 1
249 2xb
x2 β xy + y2 βx3 + y3
x2 + xy βΆ 2b2 1b
250 (x β 1)(x2 + x + 1) + 1
x β 1 β(x + 1)(x2 β x + 1) β 1
x + 1 βΆ1
x2 + 2x + 1 x6(x + 1)
x β 1
251 (x + y)2 β x2 β y2
x + y βx2 β y2
2x2y2 βΆ (x2 β y2) 1
xy(x + y)
esercizi di riepilogo considerando verificate le condizioni di esistenza
252 ππ2 β 1ππ2ππ2 β
2ππ2 + 1ππ2 +
ππ2 + 1ππ2ππ2
1 β 2ππ2
ππ2
253 οΏ½3
π₯π₯ + 2π¦π¦ β3
π₯π₯ β 2π¦π¦οΏ½ βΆ6
π₯π₯2 β 4π¦π¦2 β2π¦π¦
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 22 di 29
254 1 +2π¦π¦3 + π₯π₯3
6π₯π₯2π¦π¦2 β1π¦π¦2 β
π¦π¦3π₯π₯2 β
π₯π₯6π¦π¦2
(π¦π¦ β 1)(π¦π¦ + 1)π¦π¦2
255 π₯π₯(π₯π₯2 β 4)π₯π₯2 + 4π₯π₯ + 4 : (4π₯π₯2):
(π₯π₯ β 2)2
2π₯π₯2 β 8 1
2π₯π₯
256 οΏ½1
π₯π₯ + 2 +2π₯π₯2
π₯π₯2 + 5π₯π₯ + 6οΏ½ βΆπ₯π₯
π₯π₯2 β π₯π₯ β 6 (π₯π₯ β 3)(2π₯π₯2 + π₯π₯ + 3)
x(x + 3)
257 οΏ½ππππ2 β
ππ β 1ππ + ππ2οΏ½ : οΏ½
1ππ +
1πποΏ½
ππππ2 + ππ
258 π₯π₯2 + π¦π¦2 + 2π₯π₯π¦π¦
2π₯π₯2π¦π¦ β1π₯π₯ β
(π₯π₯ β π¦π¦)2
2π₯π₯2π¦π¦ + 3 1 + 3π₯π₯π₯π₯
259 β2ππππ + ππ + οΏ½
ππ β 2ππππ + ππ β
2ππ β ππππ β ππ + 1οΏ½ β
ππ β ππ2ππ β ππ β2
260 οΏ½π₯π₯ β 2π¦π¦
π₯π₯2 + 2π₯π₯π¦π¦ + π¦π¦2 +2
π₯π₯ + π¦π¦οΏ½ β οΏ½1π₯π₯2 +
2π₯π₯π¦π¦ +
1π₯π₯2οΏ½
6π₯π₯π¦π¦(π₯π₯ + π¦π¦)
261 ππ β π₯π₯
2ππ +115π₯π₯ β
ππ2ππ +
5π₯π₯2 β 2ππ10πππ₯π₯
2π₯π₯
262 οΏ½2π₯π₯ + 2π¦π¦
π₯π₯ +π₯π₯2 β π¦π¦2
π₯π₯π¦π¦ βπ₯π₯2 + π¦π¦2 + 2π₯π₯π¦π¦
π₯π₯π¦π¦ οΏ½ :π₯π₯ + 1
9(1β π₯π₯2) 0
263 οΏ½1
π₯π₯ + 1 +1
π₯π₯ β 3οΏ½ β(π₯π₯2 β 2π₯π₯ β 3) β οΏ½
1π₯π₯ β 1 β
1π₯π₯ + 3οΏ½
8π₯π₯ + 3
264 οΏ½1 +1π₯π₯οΏ½ β οΏ½
3π₯π₯π¦π¦ β π₯π₯ + π¦π¦ β 1 +
3π₯π₯π¦π¦ β π₯π₯ β π¦π¦ + 1οΏ½
6(π₯π₯ β 1)(π¦π¦ β 1)
265 2π¦π¦ β 10 β π₯π₯π¦π¦ + 5π₯π₯
π¦π¦(1 + π¦π¦) :(π₯π₯ β 2)(π₯π₯ + 2)π¦π¦3 β 4π¦π¦2 β 5π¦π¦ β
(π¦π¦ β 5)2
π₯π₯ + 2
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 23 di 29
266 οΏ½1
π₯π₯ + 1 β1
π₯π₯ + 3οΏ½ β οΏ½π₯π₯ +16π₯π₯ β 3 + 5οΏ½ :
π₯π₯ + 1π₯π₯2 β 9 2
267 ππ β ππππ + ππ β οΏ½
ππππ β ππ +
ππππ + ππ +
2ππ2
ππ2 β ππ2οΏ½ 1
268 π₯π₯ + 3π¦π¦
2π₯π₯ +π₯π₯ β π¦π¦π¦π¦ β
2π₯π₯ β π¦π¦3π¦π¦ β
4π₯π₯2 + 9π¦π¦2
6π₯π₯π¦π¦ β2π₯π₯ + π¦π¦
6π¦π¦
269 2π₯π₯4 β 3π¦π¦2
12π₯π₯4π¦π¦2 β2π₯π₯2 β 312π₯π₯2π¦π¦2 β
936π₯π₯4
π₯π₯2 β 2π¦π¦2
4π₯π₯4π¦π¦2
270 οΏ½1 β 2π₯π₯
1 β 4π₯π₯2οΏ½2
1
(1 + 2π₯π₯)2
271 οΏ½β32 βππ3ππππ2 οΏ½
3
β27ππ9ππ3
8ππ6
272 οΏ½1
π₯π₯2 + 2π₯π₯ + 4 +1
π₯π₯3 β 8οΏ½ : οΏ½1
π₯π₯ β 2 + 1οΏ½ β οΏ½4π₯π₯ + π₯π₯ + 2οΏ½
1π₯π₯
273 οΏ½οΏ½πππ₯π₯ +
πππ¦π¦οΏ½ :
πππ₯π₯ + πππ¦π¦π¦π¦2π₯π₯2 +
1πποΏ½ β π₯π₯π¦π¦
1ππ
274 οΏ½1 +π₯π₯2 + π¦π¦2
2π₯π₯π¦π¦ οΏ½ β οΏ½π₯π₯2 + π¦π¦2
2π₯π₯π¦π¦ β 1οΏ½ : οΏ½1π¦π¦2 β
1π₯π₯2οΏ½
2
π₯π₯2π¦π¦2
4
275 οΏ½1
π₯π₯ β 1 +1
π₯π₯ + 1 +4
π₯π₯2 β 1οΏ½ :π₯π₯2 β 4
π₯π₯2 β 3π₯π₯ + 2 2
π₯π₯ + 1
276 4π₯π₯2 + π₯π₯ + 1
3π¦π¦ β 3π₯π₯ βπ¦π¦2 β π₯π₯2
16π₯π₯4 β (π₯π₯ + 1)2 β4π₯π₯2 β π₯π₯ β 1
π₯π₯ + π¦π¦ 13
277 4π₯π₯ + 3π₯π₯2 + 3π₯π₯ +
π₯π₯2 + π₯π₯π₯π₯2 + 4π₯π₯ + 3 +
2π₯π₯
π₯π₯ + 3π₯π₯
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 24 di 29
278 οΏ½ππ β 1 +6
ππ β 6οΏ½ : οΏ½ππ β 2 +3
ππ β 6οΏ½ βππ2 β 25
ππ2 + ππ β 20 1
279 οΏ½οΏ½2π₯π₯π₯π₯ + 1 β
π₯π₯ β 1π₯π₯ οΏ½ :
π₯π₯π₯π₯2 β 1οΏ½ β
π₯π₯3
π₯π₯4 β 1 π₯π₯
π₯π₯ + 1
280 οΏ½4
ππ + 1 β5
ππ + 2οΏ½ :οΏ½1 βππ2 + 4ππ β 1ππ2 + 3ππ + 2οΏ½ 1
281 π₯π₯
π₯π₯ β π¦π¦ β οΏ½1 βπ¦π¦3
π₯π₯3οΏ½ βπ₯π₯2 + 2π₯π₯π¦π¦ + π¦π¦2
π₯π₯2 βπ¦π¦π₯π₯
282 8π₯π₯3
π₯π₯3 β π¦π¦3 β οΏ½π₯π₯2 + π₯π₯π¦π¦ + π¦π¦2
4π₯π₯2π¦π¦ οΏ½ :2π₯π₯
π₯π₯π¦π¦ β π¦π¦2 1
283 οΏ½2
3ππ2 + 6ππ +1
ππ2 β 2ππ β2
ππ2 β 4οΏ½ : οΏ½1ππ β
1ππ + 2οΏ½ β
16
284 οΏ½π¦π¦2
π₯π₯3 β π₯π₯π¦π¦2 +1
π₯π₯ + π¦π¦ βπ¦π¦
π₯π₯2 β π₯π₯π¦π¦οΏ½ : οΏ½1
π₯π₯ + π¦π¦ +π¦π¦
π₯π₯2 β π¦π¦2οΏ½ π₯π₯ β 2π¦π¦π₯π₯
285 οΏ½π₯π₯ + π¦π¦π₯π₯ β π¦π¦ β
π₯π₯ β π¦π¦π₯π₯ + π¦π¦οΏ½ : οΏ½
π₯π₯ β π¦π¦π₯π₯ + π¦π¦ +
π₯π₯ + π¦π¦π₯π₯ β π¦π¦οΏ½
2π₯π₯π¦π¦π₯π₯2 + π¦π¦2
286 ππ + 2ππ
2ππ β 4ππ +8ππ
ππ2 β 4ππ2 :8ππ
ππ β 2ππ +2ππ β ππ
4ππ + 2ππ ππ + 4ππππ β 2ππππ2 β 4ππ2
287 οΏ½π¦π¦3 β π¦π¦2 β π¦π¦ + 1
2π¦π¦ οΏ½ β οΏ½π¦π¦
π¦π¦3 β 1 βπ¦π¦
π¦π¦3 + 1οΏ½ π¦π¦ β 1
π¦π¦4 + π¦π¦2 + 1
288 οΏ½ππ β 8
ππ2 + 5ππ β 6 β2
ππ + 6 +2
ππ β 1οΏ½ β(ππ2 β 1) ππ + 1
289 οΏ½2
ππ2 β 3ππ + 2+
3ππ2 β 5ππ + 4
οΏ½ :οΏ½5ππ2 β 19ππ + 14ππ2 β 6ππ + 8
οΏ½ : οΏ½1
ππ2 + 2ππ + 1β
1ππ β 1
οΏ½ ππ2 + 2ππ + 12 β ππ β ππ3
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 25 di 29
290 οΏ½οΏ½β2
π₯π₯ + π¦π¦ +2π₯π₯ β π¦π¦π₯π₯2 β π¦π¦2οΏ½
2
:οΏ½π₯π₯2
π₯π₯2 β π¦π¦2 β 1οΏ½2
οΏ½2
1π¦π¦4
291 π₯π₯3 + π¦π¦3
(π₯π₯ + π¦π¦)3 : οΏ½2π₯π₯ β π¦π¦π₯π₯ + π¦π¦ β οΏ½
1π₯π₯ :
1π₯π₯ β π¦π¦οΏ½οΏ½ β οΏ½
π₯π₯2 β π₯π₯π¦π¦π₯π₯2 + π¦π¦2 + 2π₯π₯π¦π¦οΏ½ :
π₯π₯ β π¦π¦π₯π₯ + π¦π¦ 0
292 οΏ½οΏ½ππππ + 1οΏ½
2: οΏ½ππππ β 1οΏ½οΏ½ β οΏ½
ππππ β 1οΏ½
2: οΏ½ππππ + 1οΏ½ + 2 +
2ππππ οΏ½
ππ + ππππ
οΏ½2
293 οΏ½1
π₯π₯ + π¦π¦β
1π₯π₯ β π¦π¦
οΏ½ : οΏ½2π₯π₯
π₯π₯2 + 2π₯π₯π¦π¦ + π¦π¦2β
1π₯π₯ + π¦π¦
οΏ½ β οΏ½3π₯π₯
π₯π₯2 + 3π₯π₯π¦π¦ + 2π¦π¦2β
1π₯π₯ + π¦π¦
οΏ½ :π¦π¦
π₯π₯ + 2π¦π¦
4π¦π¦ β π₯π₯
294 οΏ½οΏ½π₯π₯ +1
π₯π₯ + 2οΏ½2
β οΏ½π₯π₯ β1
π₯π₯ + 2οΏ½2
οΏ½ β οΏ½1π₯π₯2 +
2π₯π₯3οΏ½
4π₯π₯2
295 π₯π₯2
π₯π₯3 β π¦π¦3 βπ¦π¦ β π₯π₯
π₯π₯2 + π₯π₯π¦π¦ + π¦π¦2 +1
π¦π¦ β π₯π₯ π₯π₯ οΏ½3π¦π¦ β π₯π₯π¦π¦3 β π₯π₯3
οΏ½
296 π₯π₯
π₯π₯ β 2 βπ₯π₯
π₯π₯ + 2 :4
π₯π₯2 β π₯π₯ β 2 :π₯π₯2 β 1
π₯π₯2 + π₯π₯ β 2 π₯π₯2(4 β π₯π₯)4(π₯π₯ β 2)
297 οΏ½4
2π¦π¦ + 1 +2
1 + π¦π¦ β 2π¦π¦2οΏ½ β2π¦π¦2 + 3π¦π¦ + 13 + π¦π¦ β 2π¦π¦2
21 β π¦π¦
298 ππ2 β 5ππ + 6
ππ3 β 6ππ2 + 12ππ β 8 β οΏ½4 β ππππ β 3 + 2οΏ½
1ππ β 2
299
οΏ½οΏ½π₯π₯π¦π¦ + π¦π¦π₯π₯ + 1οΏ½ : οΏ½1
π₯π₯ + 1π¦π¦οΏ½οΏ½
2
οΏ½π₯π₯3 β π¦π¦3π₯π₯2 β π¦π¦2οΏ½
2 1
300 οΏ½π₯π₯ β 4
π₯π₯2 β 5π₯π₯ + 6 βπ₯π₯ + 2
π₯π₯2 + π₯π₯ β 12οΏ½ :12
π₯π₯2 + 2π₯π₯ β 8 1
3 β π₯π₯
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 26 di 29
301 οΏ½οΏ½ππππ β
πππποΏ½
3
β οΏ½1
ππ β ππ +1
ππ + πποΏ½ β οΏ½ππ
ππ β ππ + 1οΏ½2
οΏ½β1
: οΏ½ππ
ππ + ππ βπππποΏ½
2
ππ5
2ππ4
302 1 + ππ1 β ππ β
1 β ππ1 + ππ :
1 + ππ1 β ππ β οΏ½1 β
11 + πποΏ½
3ππ3 + 5ππ(1 β ππ)(1 + ππ)2
303 οΏ½οΏ½1π₯π₯ +
1π¦π¦ β
2π₯π₯ + π¦π¦οΏ½ β οΏ½
π₯π₯π¦π¦ +
π¦π¦π₯π₯οΏ½
β1οΏ½ β
2π₯π₯2 + π¦π¦2 + 2π₯π₯π¦π¦
π¦π¦ + π₯π₯ β 2(π₯π₯ + π¦π¦)2
304 οΏ½οΏ½π₯π₯ + 1
π₯π₯2 β 7π₯π₯ + 12β
π₯π₯ + 3π₯π₯2 β 5π₯π₯ + 4
οΏ½ : οΏ½2
π₯π₯2 β 4π₯π₯ + 3+
3π₯π₯2 β 5π₯π₯ + 6
β5
π₯π₯2 β 6π₯π₯ + 8οΏ½οΏ½
8(π₯π₯ β 2)13 β 7π₯π₯
305 οΏ½οΏ½ππππ β 2 +
πππποΏ½ : οΏ½
ππππ + 2 +
πππποΏ½ + 1οΏ½
β1
β οΏ½2ππππ
ππ2 + ππ2 + 2ππππ β 1οΏ½ β12
306 οΏ½ππ β ππ2
1 + ππ +ππ
ππ2 β ππ + 1 βππ + ππ3 β ππ4
1 + ππ3 οΏ½ βππ
ππ + 1 ππ2
(ππ + 1)2
307 οΏ½οΏ½2π₯π₯
2π₯π₯ β π¦π¦ βπ¦π¦
2π₯π₯ + π¦π¦οΏ½ β4π₯π₯2 β 2π₯π₯π¦π¦16π₯π₯4 β π¦π¦4 β οΏ½1 +
π¦π¦2π₯π₯οΏ½οΏ½ :
12π₯π₯π¦π¦ β π¦π¦2 β 1 β
2π₯π₯2π₯π₯ + π¦π¦
308 οΏ½π¦π¦ β 1
π¦π¦3 + π¦π¦2 + π¦π¦ + 1+
2π¦π¦π¦π¦3 β π¦π¦2 + π¦π¦ β 1
β3
π¦π¦2 β 1οΏ½ : οΏ½
π¦π¦ + 1π¦π¦ β 1
βπ¦π¦ β 1π¦π¦ + 1
οΏ½ β1
2π¦π¦(π¦π¦2 + 1)
309 οΏ½οΏ½3π₯π₯2 β 2π₯π₯ β 1 +
6π₯π₯ β 2π₯π₯ β 3 β
9 β π₯π₯2
3π₯π₯ β 1οΏ½οΏ½
β οΏ½π₯π₯ β 1
2π₯π₯ β 3οΏ½
(π₯π₯ β 2)2
2π₯π₯ β 3
310 οΏ½2π₯π₯2 + 2π₯π₯ + 1
π₯π₯2 + π₯π₯β
π₯π₯π₯π₯ + 1
οΏ½ : οΏ½1π₯π₯2
+2π₯π₯
+ 1οΏ½ π₯π₯
π₯π₯ + 1
311 οΏ½1
π₯π₯ β 3+
12π₯π₯2 β 3π₯π₯ β 9
οΏ½ β οΏ½π₯π₯2 + 2π₯π₯2π₯π₯ + 3 οΏ½
β1
+ οΏ½1
π₯π₯2 β 9+
1π₯π₯ + 3
οΏ½ : (π₯π₯ + 3)β1 π₯π₯2 β 2π₯π₯ + 2π₯π₯2 β 3π₯π₯
312 οΏ½ππππ
+ππππ
+ 1οΏ½ : οΏ½1ππ
+1πποΏ½ :ππ3 β ππ3
ππ2 β ππ2 1
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 27 di 29
313 οΏ½οΏ½οΏ½1
π¦π¦ β 3+
11 β π¦π¦
οΏ½ β (π¦π¦2 β 4π¦π¦ + 3) β4
3π¦π¦ β 1οΏ½ β
16οΏ½2
β3π¦π¦2 β 4π¦π¦ + 1π¦π¦2 β 2π¦π¦ + 1
π¦π¦ β 1
3π¦π¦ β 1
314 1
(ππ β ππ) β οΏ½ππ + οΏ½1 βπππποΏ½ : οΏ½
1ππ
+ πποΏ½οΏ½ : οΏ½οΏ½1ππ2
+ 1οΏ½ : οΏ½1 βπππποΏ½οΏ½ β
1ππππ(ππππ + 1) ππππ β 1
ππππ
315 οΏ½1
ππ + 2ππβ
1ππ2 + 4ππ2 + 4ππππ
β οΏ½ππ β12ππ2 β 2ππ2 β 2ππππ
ππ β 2ππ οΏ½οΏ½ : οΏ½6ππ β ππππ2 β 4ππ2
+1
2ππ β πποΏ½ 1
316 οΏ½π₯π₯π¦π¦
+π¦π¦π₯π₯οΏ½ : οΏ½
π₯π₯π¦π¦
+π¦π¦π₯π₯β 2οΏ½ + οΏ½
2π₯π₯π₯π₯ β π¦π¦
β3π₯π₯2 β 2π₯π₯π¦π¦ + π¦π¦2
π₯π₯2 β π₯π₯π¦π¦οΏ½ : οΏ½
π₯π₯π¦π¦
+π¦π¦π₯π₯β 2οΏ½
π₯π₯2 + 2π¦π¦2 β π₯π₯π¦π¦(π₯π₯ β π¦π¦)2
317 οΏ½οΏ½8π₯π₯2
1 + 2π₯π₯β 2π₯π₯οΏ½ β οΏ½2π₯π₯ +
1 β 4π₯π₯ β 8π₯π₯3
4π₯π₯2 β 1 οΏ½ : οΏ½2
2π₯π₯ β 1+
42π₯π₯ + 1
β 1οΏ½οΏ½ : οΏ½π₯π₯ β2π₯π₯
2π₯π₯ + 1οΏ½
12π₯π₯ β 24π₯π₯2 β 12π₯π₯ + 1
318 οΏ½οΏ½ππ + ππππ β ππ
οΏ½2
β οΏ½ππππππ + ππ
οΏ½3
: οΏ½ππ + ππππ β ππ
οΏ½3
οΏ½ :οΏ½ππ2 β ππ2
ππ2 + ππ2 + ππππβππ3 β ππ3
ππ2 β ππ2:ππ + ππππ
οΏ½ ππ3ππ2
(ππ + ππ)3
319 ππ β ππ
(ππ2 + ππ2 + ππππ)2 + οΏ½ππ + 2ππππ β ππ
β5ππππ + ππ2
ππ2 β ππ2οΏ½3
:ππ6 + ππ6 β 2ππ3ππ3
ππ3 + 3ππ2ππ + 3ππππ2 + ππ3 0
320 3 β π₯π₯
3π₯π₯ β 1β οΏ½οΏ½
π₯π₯ + 1π₯π₯2 β 6π₯π₯ + 9
βπ₯π₯ β 2π₯π₯2 β 9
οΏ½ : οΏ½1
π₯π₯ + 3+
1π₯π₯ β 3
οΏ½οΏ½ β3
2π₯π₯
321 οΏ½1 βπ¦π¦2 β 2π¦π¦
π¦π¦2 β 2π¦π¦ + 1οΏ½ β οΏ½οΏ½(2π¦π¦ β 1)3 β
12π¦π¦ β 1
οΏ½ :8π¦π¦2 β 8π¦π¦
2π¦π¦ β 1β π¦π¦2οΏ½ 1
322 οΏ½2π₯π₯ + 1π₯π₯ + 1 :
π₯π₯π₯π₯ β 1 β
2π₯π₯2 β 1π₯π₯2 β π₯π₯ οΏ½ : οΏ½
4π₯π₯ β 1 β
3π₯π₯ + 1 β
1π₯π₯οΏ½
π₯π₯ β 5π₯π₯2 + 27π₯π₯ + 1
323
2π₯π₯ + π¦π¦ β
3π₯π₯ β π¦π¦
π₯π₯ + 5π¦π¦π₯π₯ + π¦π¦
β οΏ½
1π₯π₯ + π¦π¦ β
2π₯π₯ β π¦π¦
π₯π₯ + 3π¦π¦π₯π₯ β π¦π¦
οΏ½ 2π¦π¦
π¦π¦2 β π₯π₯2
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 28 di 29
324 οΏ½π₯π₯π¦π¦ +
4π¦π¦π₯π₯ + 4οΏ½ β οΏ½
π₯π₯3 β 2π₯π₯2π¦π¦ + 4π₯π₯π¦π¦2π₯π₯3 β 8π¦π¦3π₯π₯3 + 8π¦π¦3
π₯π₯3 + 2π₯π₯2π¦π¦ + 4π₯π₯π¦π¦2οΏ½ β
π¦π¦π₯π₯
π₯π₯ + 2π¦π¦π₯π₯ β 2π¦π¦
325
1ππ + ππ β
ππ2ππ3 β ππππ2 β
ππππ2 + ππππ
1ππ + ππ + ππ
ππ2 β ππ2 1 β
2ππππ
326 οΏ½
2π₯π₯2 + 3π₯π₯π¦π¦3π₯π₯2 β 3π₯π₯π¦π¦ β 6π¦π¦2 β οΏ½
π₯π₯2 β 2π₯π₯π¦π¦ + π¦π¦23π₯π₯ οΏ½
2π₯π₯2 + π₯π₯π¦π¦ β 3π¦π¦2π₯π₯2 β π₯π₯π¦π¦ β 2π¦π¦2
οΏ½
2
π₯π₯2 + π¦π¦2 β 2π₯π₯π¦π¦
81
327 οΏ½ 1π₯π₯2 β 4 β
2π₯π₯2 β 2π₯π₯ + 4
3π₯π₯2 + 6π₯π₯οΏ½ : οΏ½10π₯π₯ β 9
π₯π₯ β 2οΏ½1
π₯π₯ + 2 + π₯π₯ β 4π₯π₯2 β 2π₯π₯ + 4
π₯π₯2 β 2π₯π₯ + 4
6(π₯π₯2 β 2π₯π₯ β 2)
328 1 βοΏ½2π₯π₯3 + π₯π₯2 β 2π₯π₯ β 1
1 + π₯π₯ β 2π₯π₯2 + 3οΏ½3β 6π₯π₯ οΏ½π₯π₯ β 1
π₯π₯οΏ½
π₯π₯3 + 12π₯π₯ β 14π₯π₯3 β 1
π₯π₯3
329
2π₯π₯ β 1 β
3π₯π₯22π₯π₯2 β 2 οΏ½1 β π₯π₯
π₯π₯ + 2οΏ½ + 2 β π₯π₯π₯π₯ + 1 : (2 β π₯π₯)
1π₯π₯ οΏ½
3π₯π₯ + 1 β
6π₯π₯ + 2οΏ½ + 2
π₯π₯2 + π₯π₯ β 2
7π₯π₯ + 25 β π₯π₯
330
4π¦π¦π₯π₯ β π¦π¦ β
4π¦π¦2π₯π₯2 β π¦π¦2 + 2π₯π₯
π₯π₯ + π¦π¦
οΏ½2 β π¦π¦π₯π₯ + π¦π¦οΏ½ β
(2 + π₯π₯ β 2π¦π¦) β (π₯π₯ + π¦π¦)2π₯π₯2 + π₯π₯π¦π¦
2π₯π₯2
(π₯π₯ β 2π¦π¦ + 2)(π₯π₯ β π¦π¦)
331
1 + 4ππ24ππ
8ππ2 + 16ππ4 + 14ππ2
+ οΏ½1 + 1
2ππ1
4ππ + 12οΏ½
2
β1
12ππ βππ
4ππ2 + 1 1
3ππ
Algebra Frazioni algebriche
v 3.7 Β© 2020 - www.matematika.it 29 di 29
332 π₯π₯ππ β 2π₯π₯ππ + 2 β οΏ½
2π₯π₯ππ + 2 +
π₯π₯ππ
π₯π₯ππ β 2 +8
π₯π₯2ππ β 4οΏ½ ππ β β 1
333 οΏ½ππππ + ππππ
ππππ β ππππ+ππππ β ππππ
ππππ + πππποΏ½ β οΏ½1 +
ππ2ππ + ππ2ππ
2πππππππποΏ½ :
(ππππ+1 β ππππππ)(ππ2ππ + ππ2ππ)ππππβ1ππππ
ππππ + ππππ
ππ2(ππππ β ππππ)2