Question

已知A÷x²-y²/x²+4xy+4y²=x+2y/x+y,当x=2,y=1时,求A的值

Answer 1

你用括号分一下吧~

是如下所示吗?

A÷（(x²-y²)/(x²+4xy+4y²)）=(x+2y)/(x+y)

A =(x+2y)/(x+y) * (x²-y²)/(x²+4xy+4y²)

=(x+2y)(x+y)(x-y) / (x+y)(x+2y)(x+2y)

=(x-y)/(x+2y) ----(x+y)*(x+2y)≠0

当x=2,y=1时,(x+y)*(x+2y)≠0

所以A = (2-1) / (2+1*2) = 1/4