解1题：
原式=2xy/(x²-y²)+x/(x+y)
=2xy/[(x+y)(x-y)]+[x(x-y)]/[(x+y)(x-y)]
=[2xy+x(x-y)]/[(x+y)(x-y)]
=(2xy+x²-xy)/[(x+y)(x-y)]
=(x²+xy)/[(x+y)(x-y)]
=[x(x+y)]/(x+y)(x-y)]
=x/(x-y)
解2题：
原式=[a²/(a-2)-4/(a-2)]×[1/(a²+2a)]×(a²+2a)
=[(a²-4)/(a-2)]
=[(a+2)(a-2)]/(a-2)
=a+2
解3题：
原式=[1+3/(x-1)]÷[(x+2)/(x²-1)]
=[(x-1+3)/(x-1)]×[(x²-1)/(x+2)]
=[(x+2)/(x-1)]×[(x+1)(x-1)/(x+2)]
=x+1