已知xy/x+y=3,则代数式2x-7xy+2y/-x+xy-y的值是多少?

题目

已知xy/x+y=3,则代数式2x-7xy+2y/-x+xy-y的值是多少?

答案

xy=3(x+y)
[2x-7xy+2y]/[-x+xy-y]
=[2x-7*3(x+y)+2y]/[-x+3(x+y)-y]
=[2x-21x-21y+2y]/[2x+2y]
=[-19(x+y)]/[2(x+y)]
因为xy/(x+y)=3
所以x+y不等于0
所以原式=-19/2