Question

化简求值

x

x-y

+

x

x+y

-

x2

x2-y2

，其中x：y=1：3．

Answer 1

分析：先根据分式混合运算的法则把原式进行化简，再根据x：y=1：3可设x=k，则y=3k，代入原式进行计算即可．

解答：解：原式=

x

x-y

+

x

x+y

-

x2

(x-y)(x+y)

=

x(x+y)

(x-y)(x+y)

+

x(x-y)

(x-y)(x+y)

-

x2

(x-y)(x+y)

=

x(x+y)+x(x-y)-x2

(x-y)(x+y)

=

x2+xy+x2-xy-x2

(x-y)(x+y)

=

x2

(x-y)(x+y)

∵x：y=1：3
∴设x=k，则y=3k
原式=

k2

(k-3k)(k+3k)

=-

1

8

．

点评：本题考查的是分式的化简求值，解答此题时由x：y=1：3设出x=k，y=3k是解答此题的关键．