Question

已知1/x-1/y=4，求分式2x+3xy-2y/x-2xy-y的值

Answer 1

1/x-1/y=4 可得y-x=4xy
代入分式2x+3xy-2y/x-2xy-y得（2y-2x-3xy）/（y-x+2xy）=(8xy-3xy)/(4xy+2xy)
因为x≠0,且y≠0
所以分子分母同时约去xy可得值为5/6

Answer 2

解:把已知1/x-1/y=4通分得:(y-x)/xy=4，有:y-x=4xy，即
(2x+3xy-2y)/(x-2xy-y)=[2(x-y)+3xy]/(x-y-2xy)=(3xy-8xy)/(-2xy-4xy)=[-5xy]/(-6xy)=5/6