practica5 fundamentos algebra (1).docx
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Lic. Andy Pozo Gonzales
Matemáticas - Curso Propedéutico – Grupo 21
Conceptos fundamentales de AlgebraPRACTICA NO EN LINEA N° 5
1) Realizar las operaciones indicadas:
a) [(−1)n+1(−1)n−1 x
3n y−n ]
1
2n
b)n x
m x
n−1−m xn x
m−1
x2m
÷ x
n
xm
c) y2
z p∗ y
2n−2
zn− p
d)2a4−13a3b+31a2b2−38ab3+24b4
2a2−3ab+4b2
2) Dividir:
a)2 x
3+3 x2−4 x+2 x+1 b)
x6−3 y
5+4 y−5
y−2
c)4 x
3+6 x2−2 x+32 x+1 c)
x5−5 x
4+3 x3+5 x2+7 x+15 x−3
3) Hallar el valor de las expresiones sigien!es:
a) x+ y−1
x− y+1 para x=
a+1ab+1
, y=ab+a
ab+1
b) x+2a
2b− x+
x−2a
2b+ x −
4ab
4b2− x
2 parax=
ab
a+b
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Lic. Andy Pozo Gonzales
Matemáticas - Curso Propedéutico – Grupo 21
Conceptos fundamentales de Algebra
c)a
n
2n an−2nx
+ b
n
2n bn−2nx
para x=a
n+bn
2
d)a
(c−a)(a−b)+ b(a−b)(b−c )
+ c(b−c )(c−a)
") Desco#poner y si#pli$car:
a)2
3 x− 1
x2+ 3
2 x2 b)
12 x
4 x2+2 x
c) x ( x+2)
x2+4 x+4 d)
x2−9
x4−81
e) x
3+4 x2+3 x
x2+ x−6 %)
2a2
−4 ab+2b2
3 x−6÷ a−b
4 x−8
g)
16− x4
4 x+8÷ (32−8 x
2)&)
36
x+ y
6 x− y
÷
3 x
x+ y
1
x2
− y2
') Desco#poner y si#pli$car:
a)( 1 x− 1
y+ x+ y xy )∗2 xy
x+ y
b)
x2+6 x+5
x2−5 x+4
∗ x−2
x2
−4
+ x
3−2 x
x2
−4 x
c) x
2+2 x−3
x−1+3 x+12 x
− x 2−2 x+1
3 x d) x−1
x−1+ x−1
x+3− x−3
x+1
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Lic. Andy Pozo Gonzales
Matemáticas - Curso Propedéutico – Grupo 21
Conceptos fundamentales de Algebra
e)
x2−1
x2+2 x+1
∗2 x2−8 x−10
x−1
2 x+2 x
2+ x−2 ÷ x+1
x3−4 x
2−7 x+10
%)
1+ x−3
x+33− x
3 x
−
x+3 x −
x+33
x+3
x−3
−1
g)( x
3−6 x2+11 x+6
x2−9
∗ x2+2 x−3
x2−3 x+2 )÷ x
2+ x−2
x2+4 x+4
2 x2−2 x
3 x2+3 x−6
−3 x
2+12 x+122 x
&)
a
2
−1
a2+1 − a
2
+1
a2−1
a−1
a+1−
a+1a−1
÷( a2+1a −
a2−2a+1
(a−1 )2 )
i)
x2−1
x+1+ x
2+2 x+1 x+1
1
x2−3 x+2
− 1
x2+ x−6
()
2 x−2 x2
( x+1 )2 −(
x2+3 x+2( x−1 )2
− x2− x+1 x−1 )
x2+2 x+1
x2−1
+ x
2−2 x+1
( x+1 )2