Algebra
Equazioni di primo grado numeriche frazionarie
v 3.0 Β© 2016 - www.matematika.it 1 di 5
1 3
π₯π₯ β 2 = 0 ππππππππππππππππππππππ
2 4 β5
π₯π₯ = 0 π₯π₯ =
5 4
3 6
π₯π₯ β 2 = 4 π₯π₯ = 1
4 7π₯π₯ + 14
π₯π₯ β 2 = 0 π₯π₯ = β2
5 1
π₯π₯ + 1
2 = 4 π₯π₯ =
2 7
6 3
π₯π₯ β 10 + 1 = 0 π₯π₯ = 7
7 3π₯π₯ β 16 π₯π₯ =5
3 π₯π₯ = 12
8 4
3π₯π₯ β 1 = 1
2 + π₯π₯ π₯π₯ = β9
9 1
3 οΏ½9 β 42
π₯π₯ οΏ½ = 4
π₯π₯ β 6 π₯π₯ = 2
10 2π¦π¦ β 3π¦π¦2 π¦π¦ + 1 =
5
π¦π¦ + 1 β 3π¦π¦ π¦π¦ = 1
11 οΏ½4 π₯π₯ +
π₯π₯ 4οΏ½ : οΏ½
4 π₯π₯ β
π₯π₯ 4οΏ½ =
π₯π₯2 β 2π₯π₯
16 β π₯π₯2 π₯π₯ = β8
12 2
3 οΏ½1 β 2 πποΏ½ +
3 2 οΏ½1 β
3
πποΏ½ = 1 ππ = 5
13 2
π₯π₯ + 1 = 1
π₯π₯ β 3 π₯π₯ = 7
14 2
π₯π₯ + 1 = 3
π₯π₯ β 1 π₯π₯ = β5
15 π¦π¦ β 2 π¦π¦ + 1 =
π¦π¦ β 4
π¦π¦ + 3 π¦π¦ = 12
16 π₯π₯ + 1 π₯π₯ β 2 +
π₯π₯ β 1
π₯π₯ + 2 = 2 ππππππππππππππππππππππ
17 4(ππ β 3) ππ + 3 β 4 =
3
ππ β 3 ππ =
7 3
18 1
1 β π₯π₯ + 1
π₯π₯ β 1 = 1 ππππππππππππππππππππππ
19 1
π₯π₯ β 3 = β 2
π₯π₯ + 5 π₯π₯ =
1 3 20 π₯π₯ β 1
π₯π₯ + 1 β π₯π₯ + 1 π₯π₯ β 1 +
8
π₯π₯2 β 1 = 0 π₯π₯ = 2
21 4
π₯π₯ β 4 = 4
π₯π₯ + 4 ππππππππππππππππππππππ
Algebra
Equazioni di primo grado numeriche frazionarie
v 3.0 Β© 2016 - www.matematika.it 2 di 5
22 1
π₯π₯2β 3π₯π₯ + 1 π₯π₯2+ π₯π₯ =
4
π₯π₯2 β 2π₯π₯ β 3 ππππππππππππππππππππππ
23 π¦π¦ + 2 π¦π¦ β 4 =
π¦π¦ + 1
π¦π¦ β 3 π¦π¦ = 1
24 π§π§ + 1 π§π§ β 1 β
2π§π§ β 2 π§π§ + 1 =
π§π§ + 1
1 β π§π§ π§π§ = 0
25 1 + 3π₯π₯
π₯π₯ + 4
π₯π₯ β 2π₯π₯2 = 6π₯π₯
2π₯π₯ β 1 π₯π₯ = β5
26 2π¦π¦
π¦π¦ β 2 β
1 β π¦π¦
2π¦π¦ β π¦π¦2β 2 =1
π¦π¦ π¦π¦ = β32
27 π₯π₯ + 1 π₯π₯ β 1 β
3 + 6π₯π₯ π₯π₯ + 1 =
3π₯π₯ β 5π₯π₯2+ 6
(π₯π₯ + 1)(π₯π₯ β 1) ππππππππππππππππππππππ
28 1
2 β 3π§π§ β 6 3π§π§2β 2π§π§ =
5
π§π§ π§π§ =
1 4
29 1
π₯π₯2β 4 β
1
(π₯π₯ + 2)(π₯π₯ β 1) =
2
(π₯π₯ β 1)(π₯π₯ β 2) π₯π₯ = β32
30 1 + π¦π¦ π¦π¦ + 3 +
π¦π¦ + 1 π¦π¦ β 3 =
2(π¦π¦2+ 3) π¦π¦2β 9 β
1
π¦π¦ + 3 ππππππππππππππππππππππ
31 π₯π₯ + 12
π₯π₯ βπ₯π₯ β 12
π₯π₯ = 1 π₯π₯ = 1
32 π₯π₯2 + 3
π₯π₯ + 4 = π₯π₯ β 2 π₯π₯ =
11 2
33 π₯π₯
2(π₯π₯ + 1) = π₯π₯2
π₯π₯ + 1 β π₯π₯ β 1 π₯π₯ = β
2 5
34 5π₯π₯
2π₯π₯ + 3 = 1 + 3π₯π₯
2π₯π₯ β 3 π₯π₯ =
3 8 35 2π₯π₯ β 4
2π₯π₯ + 2 = π₯π₯ π₯π₯ + 1 β
1
π₯π₯ π₯π₯ = 1
36 3 οΏ½1
2(π₯π₯ β 1) +4 π₯π₯οΏ½ =
1 + 3π₯π₯
2 π₯π₯ = 6
37 2
1 β 2ππ + 1 2ππ β 1 =
1 β 5ππ
1 β 4ππ2 ππ = 0
38 2
π§π§ + 2 β 6 3 β π§π§ =
32
π§π§ + 6 β π§π§2 π§π§ = β
19 4
39 1
π₯π₯2+ 4π₯π₯ + 3 β
1
π₯π₯2β 2π₯π₯ β 3 = 1
π₯π₯2 β 9 π₯π₯ = β7
40 1
π₯π₯2β 1 β 1
π₯π₯ β π₯π₯2 = 2
π₯π₯2 + π₯π₯ ππππππππππππππππππππππ
41 4
π§π§ + 1 β 3π§π§ π§π§ β 3 =
9π§π§
9 β 3π§π§ ππππππππππππππππππππππ
Algebra
Equazioni di primo grado numeriche frazionarie
v 3.0 Β© 2016 - www.matematika.it 3 di 5
42 1
2π₯π₯ β 4 β 2 π₯π₯ + 2 =
π₯π₯ + 5
3π₯π₯2 β 12 π₯π₯ =
20 11
43 10
(π₯π₯ β 5)2+ π₯π₯
π₯π₯ β 1 = 1 ππππππππππππππππππππππ
44 4 + π₯π₯ π₯π₯ β 3 β
3 + π₯π₯ π₯π₯ β 2 =
5
π₯π₯2 β π₯π₯ β 6 ππππππππππππππππππππππ
45 π₯π₯ + 5 π₯π₯ + 3 β
3π₯π₯ π₯π₯ + 2 =
6 β 2π₯π₯2
π₯π₯2 + 5π₯π₯ + 6 π₯π₯ = 2
46 2 β π₯π₯ 3π₯π₯ + 6 +
1 β 3π₯π₯
2 + π₯π₯ = 2 π₯π₯ = β
7 16
47 1
π₯π₯2 β 9 = 3 π₯π₯ + 3 β
2
2π₯π₯ + 6 π₯π₯ =
7 2
48 1
3(π₯π₯ + 4) + 4 3π₯π₯ =
π₯π₯ β 1
8π₯π₯ + 2π₯π₯2 π₯π₯ = β5
49 2
π₯π₯2 β π₯π₯ β 1 π₯π₯2 + π₯π₯ =
4
(π₯π₯ β 1)(π₯π₯ + 1) ππππππππππππππππππππππ
50 2
π₯π₯2 β 1 = 3 π₯π₯2β 4 β
1
π₯π₯2+ π₯π₯ β 2 π₯π₯ = β7
51 3π₯π₯ β 12
π₯π₯2β 16 = 0 ππππ π₯π₯ = 4: ππππππ ππππππππππππππππππππππ
52 οΏ½ 3
2π₯π₯ β 2 β 3 2π₯π₯ + 2οΏ½ οΏ½
1 2π₯π₯ β
1 2οΏ½ +
1 2π₯π₯ + 2 =
1
π₯π₯ π₯π₯ = β5
53 1
2π₯π₯ β π₯π₯2+ 1 π₯π₯2β 4 =
2
π₯π₯2+ 2π₯π₯ π₯π₯ = 1
54 1
2π§π§ + 4 β 1 4 β 2π§π§ =
π§π§ + 1
(π§π§ + 2)(π§π§ β 2) ππππππππππππππππππππππ
55 5
π¦π¦3β 1 + π¦π¦
π¦π¦2+ π¦π¦ + 1 = 1
π¦π¦ β 1 π¦π¦ = 2
56 1
π₯π₯2+ 4π₯π₯ + 3 = 3
18 β 2π₯π₯2+ 1
π₯π₯2β 2π₯π₯ β 3 ππππππππππππππππππππππ 57 π₯π₯ β 2
π₯π₯3β π₯π₯ + 1 π₯π₯2β 1 =
2 π₯π₯2 + π₯π₯
ππππππ π₯π₯ β 0, π₯π₯ β Β±1
πππππππππ§π§ππππππππ ππππππππππππππππππππππππππ
58 4
3π₯π₯ β 4 β 4 3π₯π₯ + 4 =
6(2π₯π₯ + 5) 9π₯π₯2β 16 β
1
3π₯π₯ β 4 π₯π₯ =
2 3 59 2(π₯π₯2+ 2)
π₯π₯2β 4 β 1 = π₯π₯ + 1
π₯π₯ β 2 ππππ π₯π₯ = Β±2: ππππππ ππππππππππππππππππππππ
Algebra
Equazioni di primo grado numeriche frazionarie
v 3.0 Β© 2016 - www.matematika.it 4 di 5
60 3
π₯π₯ + 3 = οΏ½ π₯π₯ β 3 π₯π₯ + 3 β
π₯π₯ + 3 π₯π₯ β 3οΏ½ : οΏ½
π₯π₯ β 3
π₯π₯ + 3 + 1οΏ½ π₯π₯ = β1
61 1
π₯π₯2 + 2π₯π₯ β 3 β
1
π₯π₯2β 3π₯π₯ + 2 = β
1
(π₯π₯ β 2)(π₯π₯ + 3) π₯π₯ = 6
62 2π₯π₯
π₯π₯2 + 1 = οΏ½ π₯π₯ + 1 π₯π₯ β 1 β
π₯π₯ β 1 π₯π₯ + 1οΏ½ : οΏ½
π₯π₯ β 1 π₯π₯ + 1 +
π₯π₯ + 1
π₯π₯ β 1οΏ½ βπ₯π₯ β Β±1
63 2 + π₯π₯ π₯π₯ + 2 +
π₯π₯ + 1 π₯π₯ β 2 =
2(π₯π₯2+ 2)
(π₯π₯ β 2)(π₯π₯ + 2) ππππππππππππππππππππππ
64 2
π₯π₯2β π₯π₯ β 2 +
1
3π₯π₯2+ 2π₯π₯ β 1 =
7π₯π₯ β 11
3π₯π₯3β 4π₯π₯2 β 5π₯π₯ + 2 ππππππππππππππππππππππ 65 4π₯π₯ β π₯π₯2
π₯π₯4β 16 + 1 4π₯π₯ β 8 =
1
4π₯π₯ + 8 π₯π₯ = β1
66
1π₯π₯ +1 1 3 π₯π₯ β1
3
:π₯π₯2 + 3π₯π₯ 3π₯π₯ β 9 β
π₯π₯ 3 +
2π₯π₯ β 3
6 = 2 π₯π₯ = β6
5
67
π¦π¦ β 2 +1 1 π¦π¦ + 2 π¦π¦ + 2 β1 1
π¦π¦ β 2
= 2 π¦π¦ = β4
68 π₯π₯ + 12
π₯π₯ β 12= 2 βπ₯π₯ + 4
π₯π₯ β 4 π₯π₯ =89
69 1 β 2π§π§ π§π§2+ 3π§π§ +
4π§π§ β 6 2π§π§2β 6π§π§ +
12
9 β π§π§2 = 0 π§π§ = β6
70 ππ + 2 ππ2β 2ππ β
8 ππ2β 4 =
2ππ ππ2 β 4 β
ππ β 2
ππ2β 2ππ ππππππππππππππππππππππ
71 β4
π₯π₯ β 4 1 β π₯π₯ β
5
π₯π₯ + π₯π₯2 = 5
π₯π₯2β 1 π₯π₯ =
3 2
72 2π₯π₯
π₯π₯2β 3π₯π₯ + 12
9 β π₯π₯2 = 2π₯π₯ π₯π₯2+ 3π₯π₯
ππππππ π₯π₯ β β3
πππππππππ§π§ππππππππ ππππππππππππππππππππππππππ
73 1
5π§π§ + 5 + 1 5π§π§ β 5 +
1 5 =
π§π§2 + 5
5 + 5π§π§2β 10π§π§ π₯π₯ = β
1 2
74 3
π₯π₯2β π₯π₯ + 3 π₯π₯2+ π₯π₯ +
3 π₯π₯ =
π₯π₯ β 3π₯π₯2
π₯π₯ β π₯π₯3 π₯π₯ =
3 7 75 π₯π₯ β 3
π₯π₯ + 1 = β5
2π₯π₯ β 1
π₯π₯ + 1 π₯π₯ =
8 11
76 3
π₯π₯ β 1 = 2
3 π₯π₯ =
11 2
Algebra
Equazioni di primo grado numeriche frazionarie
v 3.0 Β© 2016 - www.matematika.it 5 di 5
77 1
2π₯π₯ β 1 = 1 π₯π₯ β
1
2π₯π₯ + 2 π₯π₯ = 2
78 π₯π₯
2π₯π₯ + 6 = 1 2 +
π₯π₯ + 1
π₯π₯ + 3 π₯π₯ = β
5 2 79 2π₯π₯ β 6
π₯π₯2β 2π₯π₯ β 15 = 1 π₯π₯ + 3 +
2
π₯π₯ β 5 π₯π₯ = β7
80 π₯π₯2 2 β 9
π₯π₯ β 3 4π₯π₯ β 6 +
2π₯π₯3 3 β 2π₯π₯ =
6π₯π₯2β 9π₯π₯
6 β 4π₯π₯ ππππππππππππππππππππππ
81 π₯π₯
π₯π₯ β 3 = π₯π₯ π₯π₯ + 3 +
2
π₯π₯2β 9 + 1 β π₯π₯2
π₯π₯2β 9 π₯π₯ = β
7 6
82 π₯π₯
π₯π₯ β 5 = 2
π₯π₯2β 25 + 1 π₯π₯ = β
23 5
83 π₯π₯
π₯π₯ + 1 =
2π₯π₯ + 1 2π₯π₯ + 2 +
3
π₯π₯2β 1 π₯π₯ = β5
84 6π₯π₯ + 4 4π₯π₯2+ 4π₯π₯ + 1 β
4π₯π₯ 4π₯π₯2β 1 =
1 2π₯π₯ + 2 β
2
4π₯π₯2β 1 π₯π₯ = β
3 4
85 π₯π₯2
π₯π₯2β 5π₯π₯ β 14 + 3π₯π₯ π₯π₯ + 2 +
2π₯π₯ π₯π₯ β 7 =
5π₯π₯ + 6
π₯π₯ + 2 + 1 π₯π₯ = β
56 17 86 π₯π₯ + 7
π₯π₯ + 2 + π₯π₯ =
π₯π₯2β 1 π₯π₯ + 1 β
1 π₯π₯ + 2 β
3 β 2π₯π₯2
π₯π₯2+ π₯π₯ + 2 ππππππππππππππππππππππ 87 π₯π₯2β 1
π₯π₯2β π₯π₯ = π₯π₯ π₯π₯ β 4 β
3π₯π₯2
π₯π₯(π₯π₯ β 1)(π₯π₯ β 4) ππππππππππππππππππππππ
88 1
βπ₯π₯2+ 2π₯π₯ β 1 = β 3 π₯π₯ β 1 β
2
3π₯π₯ β 3 π₯π₯ =
14 11 89 4π₯π₯ β 1
4π₯π₯2β 1 = β
3π₯π₯ + 5 1 β 2π₯π₯ +
1 β 3π₯π₯
2π₯π₯ + 1 π₯π₯ = β
5 14
90 π₯π₯
π₯π₯ + 1 = 1 3π₯π₯ + 3 +
2
3 π₯π₯ = 3
91 2π₯π₯
π₯π₯ β 3 β π₯π₯2 π₯π₯ β 2 +
3π₯π₯ β π₯π₯2 2 β π₯π₯ =
π₯π₯ β π₯π₯2
π₯π₯2β 5π₯π₯ + 6 π₯π₯ = 0
92 2π₯π₯ + 1 π₯π₯ + 1 +
5 1 β π₯π₯ =
2
π₯π₯2β 1 π₯π₯ = 4
93 5 +4 β 2π₯π₯ π₯π₯ + 2 +
5 1 β π₯π₯ =
3π₯π₯ + 2
π₯π₯ β 1 π₯π₯ = β14
94 5
4π₯π₯2β 4π₯π₯ + 1 β 1
(2π₯π₯ + 1)2β 3
(4π₯π₯2β 1)2 = 20π₯π₯2+ 27 16π₯π₯4β 8π₯π₯2+ 1 β
1
4π₯π₯2 β 1 π₯π₯ =
9 8