问题 解答题
(1)计算:
x
x-y
y2
x+y
-
x4y
x4-y4
÷
x2
x2+y2

(2)解分式方程:
x
x+2
-
x+2
x-2
=
8
x2-4
答案

(1)原式=

x
x-y
y2
x+y
-
x4y
(x2+y2)•(x2-y2)
x2+y2
x2
=
xy2
(x+y)(x-y)
-
x2y
(x+y)(x-y)
=
xy2-x2y
(x+y)(x-y)
=
xy(y-x)
(x+y)(x-y)
=-
xy
x+y

(2)方程两边同乘以最简公分母(x+2)(x-2),

得:(x-2)x-(x+2)2=8,

x2-2x-x2-4x-4=8,

-6x=12

∴x=-2,

经检验:x=-2不是原方程的根,

∴原方程无解.

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