先化简,再求值(x-y+y^2/x+y)÷x^2,其中x、y满足|x-2y+1|+|2x-y-5|=0

题目

先化简,再求值(x-y+y^2/x+y)÷x^2,其中x、y满足|x-2y+1|+|2x-y-5|=0
如题

答案

根据绝对值为非负数得
x-2y+1=0
2x-y-5=0
联立解得
x=11/3 y=7/3
[x-y+y^2/(x+y)]÷x^2
=[(x-y)(x+y)+y^2]/(x+y)÷x^2
=(x²-y²+y²)/(x+y)÷x^2
=1/(x+y)
=1/(11/3+7/3)
=1/6