2xy/x²-y²+x/x+y .（a²/a-2-4/a-2）乘1/a²+2a.

2xy/x²-y²+x/x+y
=[(2xy+x(x-y)]/(x²-y²)
=[2xy+x²-xy]/(x²-y²)
=[xy+x²]/(x²-y²)
=[x(x+y)]/(x-y)(x+y)
=x/(x-y)
（a²/a-2-4/a-2）乘1/a²+2a
=（(a²-4)/(a-2)）*1/a(a+2)
=(a+2)*1/a(a+2)
=1/a
（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

2xy/(x²-y²)+x/(x+y)=2xy/[(x+y)(x-y)]+x(x-y)/[(x+y)(x-y)]=[2xy+(x²-xy)]/[(x+y)(x-y)]
=[x(x+y)]/[(x+y)(x-y)]=x/(x-y)
[a²/(a-2)-4/(a-2)]*[1/(a²+2a)]=[(a²-4)/(a-2)]/[a(a+2)]=(a+2)/[a(a+2)]=1/a
[1+3/(x-1)]÷[(x+2)/(x²-1)]=[(x+2)/(x-1)][(x+1)(x-1)/(x+2)]=x+1