Ejercicios de fracciones algebraicas (con solución):
1
EJERCICIOS PARA 4º A-B (MATEMÁTICAS B) ENTREGAR EL MARTES 18-11-08 NOMBRE: 1. Efectúa las siguientes operaciones y obtén en cada caso la fracción irreducible: a) = - + ⋅ + 1 4 4 1 2 2 2 2 x x x x x 1 4 ) 1 ( ) 1 ( ) 1 ( ) 1 ( 4 ) 1 ( 2 2 - = + ⋅ - ⋅ + + ⋅ ⋅ + ⋅ x x x x x x x x b) = - ⋅ - - 12 4 5 5 1 6 2 2 x x x x ) 1 ( 2 5 ) 3 ( 4 ) 1 ( ) 1 ( ) 1 ( 5 ) 3 ( 2 - ⋅ = - ⋅ ⋅ + ⋅ - ⋅ ⋅ - ⋅ x x x x x x c) = - - - + - 9 3 1 : 6 2 1 2 x x x x ) 1 ( 2 3 ) 1 ( ) 1 ( ) 3 ( 2 ) 3 ( ) 3 ( ) 1 ( + ⋅ - = + ⋅ - ⋅ + ⋅ ⋅ - ⋅ - x x x x x x d) = - + - + + 4 8 4 6 2 : 9 6 2 2 2 x x x x x x x x x x x x x x x ) 1 ( ) 3 ( 2 ) 3 ( 2 ) 1 ( ) 1 ( 4 ) 3 ( 2 2 - ⋅ + ⋅ = + ⋅ ⋅ - ⋅ - ⋅ ⋅ + 2. Realiza las operaciones combinadas siguientes dando el resultado en la forma más simplificada posible: a) = - - + x x x x 2 4 : 2 1 2 2 1 ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( : 2 = + ⋅ ⋅ + = - ⋅ + ⋅ - + x x x x x x x x x x b) = - - ⋅ - + x x x x x x x x x 2 2 2 2 2 12 3 1 2 16 : 4 ) 1 ( ) 1 ( 3 ) 1 ( ) 4 ( 3 ) 4 ( ) 4 ( ) 1 ( ) 4 ( 2 2 2 2 - ⋅ + ⋅ = - ⋅ - ⋅ ⋅ + ⋅ - + ⋅ + ⋅ x x x x x x x x x x x x c) = - ⋅ - 1 1 1 x x x 1 1 1 = - ⋅ - x x x x d) = - - - + 1 : 1 x x x x x x = - - - = - - - - + - 1 2 : 1 1 : 1 2 2 2 2 x x x x x x x x x x x x x 2 ) 2 ( ) 1 ( ) 1 ( 2 - = - ⋅ ⋅ - - ⋅ = x x x x x x x e) = - + ⋅ - 3 9 3 3 3 x x x x x ( 3 9 ) 3 ( ) 3 ( 3 ) 9 ( ) 3 ( ) 3 ( 3 ) 9 ( 3 9 2 2 2 2 + ⋅ + = - ⋅ + ⋅ + ⋅ - = - + ⋅ ⋅ - x x x x x x x x x x x f) = - - + ⋅ + 1 1 1 1 2 1 x x x x ) 1 ( 1 ) 1 ( 2 2 ) 1 ( ) 1 ( 1 1 2 1 - ⋅ - = - ⋅ ⋅ - = - ⋅ + - - - ⋅ ⋅ + x x x x x x x x x x
description
Se detallan las soluciones de los ejercicios propuestos.
Transcript of Ejercicios de fracciones algebraicas (con solución):
EJERCICIOS PARA 4º A-B (MATEMÁTICAS B) ENTREGAR EL MARTES 18-11-08
NOMBRE: 1. Efectúa las siguientes operaciones y obtén en cada caso la fracción irreducible:
a) =−+⋅
++
1
44
1 2
2
2
2
x
x
x
xx
1
4
)1()1()1(
)1(4)1(2
2
−=
+⋅−⋅++⋅⋅+⋅
x
x
xxx
xxx
b) =−+⋅
−−
124
55
1
622 x
x
x
x
)1(2
5
)3(4)1()1(
)1(5)3(2
−⋅=
−⋅⋅+⋅−+⋅⋅−⋅
xxxx
xx
c) =−−
−+−
93
1:
62
1 2
x
x
x
x
)1(2
3
)1()1()3(2
)3()3()1(
+⋅−=
+⋅−⋅+⋅+⋅−⋅−
xxxx
xx
d) =+−
+−
++484
62:
9622
2
xx
x
xx
xx
x
xx
xxx
xx )1()3(2
)3(2)1(
)1(4)3( 22 −⋅+⋅=+⋅⋅−⋅
−⋅⋅+
2. Realiza las operaciones combinadas siguientes dando el resultado en la forma más simplificada posible:
a) =−−
+xx
x
x 2
4:
21
2
2
1)2(
)2(
)2(
)2()2(:
2 =+⋅
⋅+=−⋅
+⋅−
+xx
xx
xx
xx
x
x
b) =−−⋅
++−+
xx
x
xx
x
x
xx22
2
2
2 123
12
16:
4
)1(
)1(3
)1(
)4(3
)4()4(
)1()4(2
22
2 −⋅+⋅=
−⋅−⋅⋅
+⋅−+⋅+⋅
xx
x
xx
x
xx
x
x
xx
c) =−
⋅
−1
11
x
x
x1
1
1 =−
⋅−x
x
x
x
d) =
−−
−+
1:
1 x
xx
x
xx =
−−
−=
−−−
−+−
1
2:
11:
1
2222
x
xx
x
x
x
xxx
x
xxx
2)2()1(
)1(2
−=
−⋅⋅−−⋅=
x
x
xxx
xx
e) =−+⋅
−3
93
3
3
x
xx
x
x ( )3
9)3(
)3(3
)9()3()3(
3
)9(
3
9 2222 +⋅+=−⋅
+⋅+⋅−=−
+⋅⋅
− xx
x
xxx
x
xx
x
x
f) =
−−
+⋅+
1
1
1
1
2
1
xxx
x
)1(
1
)1(2
2
)1()1(
11
2
1
−⋅−=
−⋅⋅−=
−⋅+−−−⋅
⋅+
xxxxxx
xx
x
x
