Question

先化簡，再求值：當x=2，y=-1時，求

xy2

x2-y2

-

x4y

x4-y4

÷

x2

x2+y2

的值．

Answer 1

分析：將除法轉化為乘法，然后將分式因式分解，約分后再通分．

解答：解：原式=

xy2

x2-y2

-

x4y

(x2-y2)•(x2+y2)

•

x2+y2

x2

=

xy2

x2-y2

-

x2y

x2-y2

=

xy2-x2y

x2-y2

=

xy(y-x)

(x-y)(x+y)

=-

xy

x+y

原式=-

2×(-1)

2+(-1)

=2．

點評：本題考查了分式的化簡求值，學會通分、約分及因式分解是解題的關鍵．