(1)
(1+x)/(x²+x-2)÷[（x-2)+3/(x+2)]
=[(x+1)/(x^2+x-2)]/[(x^2-1)/(x+2)]
=(x+1)(x+2)/[(x^2+x-2)(x^2-1)]
=(x+1)(x+2)/[(x+2)(x+1)(x-1)^2]
=1/(x-1)^2
=1/(3-1)^2
=1/4
(2)
(|x|-1)/[(x-3)(x+1)],分式有意义,分母不等于0
(x-3)(x+1)≠0
x≠3且x≠-1
(3)
题目好像有点问题,最后一项分母是-a吗?
(4)
M/(x^2-y^2)=(2xy-y^2)/(x^2-y^2)+(x-y)/(x+y)
M=(2xy-y^2)+(x-y)^2
=2xy-y^2+x^2-2xy+y^2
=x^2