①- x+2y分之x-y 除以 x的平方+4xy+4y的平方分之x的平方-y的平方 ②4-4x+x的平方分之2x-6 除以

题目

①- x+2y分之x-y 除以 x的平方+4xy+4y的平方分之x的平方-y的平方 ②4-4x+x的平方分之2x-6 除以
（x-2)(x+3）分之3-x

答案

①- x+2y分之x-y 除以 x的平方+4xy+4y的平方分之x的平方-y的平方
= -(x-y)/(x+2y) ÷ (x^2-y^2)/(x^2+4xy+4y^2)
= -(x-y)/(x+2y) ×(x^2+4xy+4y^2)/(x^2-y^2)
= -(x-y)/(x+2y) ×(x+2y)^2/[(x+y)(x-y)]
= -(x+2y)/(x+y)
②4-4x+x的平方分之2x-6 除以（x-2)(x+3）分之3-x
= (2x-6)/(4-4x+x^2) ÷ (3-x)/[(x-2)(x+3)]
= 2(x-3)/(x-2)^2 × (x-2)(x+3)/(3-x)
= 2(x-3)/(x-2)^2 × (x-2)(x+3)/[-(x-3)]
= -2(x+3)/(x-2)