先化简,再求值:x-y分之x+y÷(x+y)²,其中x=4,y=-2.

问题描述:

先化简,再求值:x-y分之x+y÷(x+y)²,其中x=4,y=-2.

x²-y²)/(x+y)-2x-2y
=(x+y)(x-y)/(x+y)-2x-2y
=x-y-2x-2y
=-x-3y
把x=3,y=1/3代入得
原式=-3-3*(1/3)=-4

=(x+y)/(x-y)×1/(x+y)²
=1/(x+y)(x-y)
=1/(x²-y²)
当x=4,y=-2时
原式=1/(16-4)=1/12