已知（x分之1）+（y分之1）=3,求（2x-3xy+2y）分之（x+2y+y）的值

题目

已知（x分之1）+（y分之1）=3,求（2x-3xy+2y）分之（x+2y+y）的值

答案

1/x+1/y=(x+y)/xy=3
x+y=3xy
(2x-3xy+2y)/(x+2xy+y)
=[2(x+y)-3xy]/[(x+y)+2xy]
因为x+y=3xy,带入
=(6xy-3xy)/(3xy+2xy)
=3xy/5xy
=3/5