001- Quattro equazioni di primo grado con frazioni
Equazione A
(da Flaccavento-Romano, Obiettivi e metodi, Algebra, Fabbri)
( ) ( )
3 1
3
2 1
3 1 4 2 3
6 x− − x + = − x+
risoluzione
( ) ( ) ( )
6 1 2 2 1
6
6 4 2 3 6
6 6 4 2 6 8 12
6 4 8 6 12 6 2
10 2 2 10
1 5
x x x
x x x
x x x
x x
− − +
= − +
− − − = − −
− + = − + +
=
= =
verifica
1° membro
3 1 5 1
3
2 1 5 1
3 3 1 5
5 3
2 5 5 3 3 4
5 3
7 5 3 12
5 1 3
7 5
1 3 12
15 7 15
19 15
−
− ⋅ +
=
=
−
− +
=
=
−
− =
= − ⋅ − ⋅ =
= − − = −
2° membro
1
4 2 1 5 3
6 1
4 2 15 5 6
1
4 17 5
6 1
68 5
6 1 68 5
1 6 1 34
15
15 34 15
19 15
−
⋅ +
= −
+
=
− ⋅
= − = − ⋅ =
− = − = −
Equazione B
(da Flaccavento-Romano, Obiettivi e metodi, Algebra)
( ) ( )
x + − x − x x
− − = −
1 10
2 2 15 15
11 3
2 7 32 15
risoluzione
( ) ( ) ( ) ( )
3 1 4 2 15 10 11
30
4 7 32 30 3 3 8 60 10 110 28 128
3 8 10 28 128 3 60 110
43 301 301
43 7
x x x x
x x x x
x x x x
x x
+ − − − − = −
+ − + − + = −
− − − = − − − −
− = −
= −− = +
verifica
1° membro
( )
( )
( )
7 1 10
2 2 7 15 15
7 11 3 8
10
2 14 15 15
4 3 4
5
2 1 15
4 3 4
5 2 15
4 3
12 2 20 15
34 15 + − ⋅ − − − =
= − − − − =
= − −
+ =
= + + = + + =
2° membro
( )
( )
2 7 7 32 15 2 49 32
15 2 17
15
34 15
⋅ − =
− =
⋅ =
Equazione C
(Da Linardi-Galbusera, Percorsi di Algebra, Mursia)
2 1
3
2 2
1 5
2 5 x − − − = + +x x
risoluzione
( ) ( ) ( )
10 2 1 15 2 30
6 1 12
30 20 10 30 15 6 6 12 20 15 6 6 12 10 30 29 58
58 29 2
x x x
x x x
x x x
x x
− − −
= + +
− − + = + + + − = + + +
=
= =
verifica
1° membro
2 2 1 3
2 2 2 4 1
3 0 3
3 1
⋅ − − − =
− − = =
2° membro
2 1 5
2 5 3
5 2 5
5 5 1 + + =
+ = =
Equazione D
(da Flaccavento-Romano, Obiettivi e metodi, Algebra, Fabbri)
( )
3 1 4
2 1
3
5 2 3
7 1
8
− x − x + = − − −x x
risoluzione
( ) ( ) ( ) ( )
18 1 8 2 1 24
8 5 2 3 7 1 24
18 18 16 8 40 16 21 3 18 16 16 21 40 3 18 8 3 33
33 3 11
− − +
= − − −
− − − = − − +
− − + + = + − +
=
= =
x x x x
x x x x
x x x x
x x
Verifica
1° membro
( )
( )
3 1 11 4
2 11 1 3 3 10
4
23 3
30 4
23 3 15
2 23
3
45 46 6
91 6
− − ⋅ + =
= −
− = − − =
= − − = − − = −
2° membro
5 2 11 3
7 11 1 8 5 22
3
77 1 8 17
3 76
8
17 3
19 2 34 57
6
91 6
− ⋅ − ⋅ − =
= − − − =
= − − = − − =
= − − = −
002 -Equazioni di primo grado con frazioni
Equazione A
( )
3 1 4
1 2
2 2 3 5
3 2 x− − = x+ − +x
risoluzione
5 3 1 10 20
8 2 3 10 3 20
15 5 10 16 24 10 30 15 16 10 24 30 5 10
9 9
9 9 1
( x ) ( x ) (x )
x x x
x x x
x x
− − = + − +
− − = + − −
− + = − + +
=
= =
verifica
3 1 1 4
1 2 2
4 1 2
1 2
1 2 0
⋅ − − =
= − = − =
( )
( )
2 2 1 3 5
1 3 2 2 2 3
5
4 2 2 5
5 2 1
10
5 2 2 2 0
⋅ + − + =
+ − =
⋅ − = − = − =
Equazione B
( )
2 3
2
3 2
4
1 3
2 3 x+ − + = − −x x
risoluzione
( ) ( ) ( )
6 2 3 9 2
12
4 4 2 12 12 18 9 18 4 8 4
12 9 4 4 8
4 4
x x x
x x x
x x x
x x
+ − + = − −
+ − − = − +
− − = −
− = −
= verifica
( )
2 4 3 2
3 4 2 4 8 3
2
3 6 4
11 2
18 4
11 2
9 2
2 2 1
⋅ + − + =
+ − ⋅ = − = − = =
1 3
2 4 3 1 3
2 3
1 3
2 3
3 3 1
− − =
= − − = + = =
Equazione C
( )
2 3
15
2 1 3
2 5 x+ = x+ − −x
Risoluzione
( ) ( ) ( )
2 3
15
5 2 1 3 2
15
2 6 10 5 3 6
2 10 3 5 6 6
5 5 5
5 1
x x x
x x x
x x x
x x
+ = + − − + = + − +
− + = + −
− =
= − = −
Verifica
( )
2 1 3 15
2 2 15
4 15
− + = ⋅ = 2
( )
1 13
1 2 5 2 1
3
3 5
1 3
3 5 5 9
15
4 15
− + − − − =
− + − − = − + =
− + =
