已知1/x+1/y=5,求分式2x-3xy+2y/x+2xy+y的值

题目

已知1/x+1/y=5,求分式2x-3xy+2y/x+2xy+y的值

答案

1/x+1/y=5
y+x=5xy
x+y=5xy
所以
2x-3xy+2y/x+2xy+y
=[2(x+y)-3xy]/[(x+y)+2xy]
=(2*5xy-3xy)/(5xy+2xy)
=7xy/7xy
=1