1.(4a/a-2-a/a+2)÷1/a^2-4=〔4a(a+2)/(a-2)(a+2)-a(a-2)/(a-2)(a+2)〕*（a+2）（a-2）
=(3a^2+10a)/(a-2)(a+2))〕*（a+2）（a-2）
=3a^2+10a
2.[(a-1/a^2-4a+4)-(a+2/a^2-2a)]÷（4/a-1)=〔a(a-1)/a(a-2)^2-(a^2-4)/a(a-2)^2〕*a/4-a
=〔（4-a)/a(a-2)^2〕*a/4-a
=1/(a-2)^2
3.(1/a-1)-(2/1-a^2)=1/(a-1)+2/(a^2-1)
=(a+1)/(a^2-1)+2/(a^2-1)
=(a+3)/(a^2-1)
4.(a+b/ab)-(b+c/bc)=c(a+b)/abc-a(b+c)/abc
=b(c-a)/abc
=(c-a)/ac
5.[3x/(x-3)^2]-(x/3-x)=3x/(3-x)^2-(x/3-x)
= 3x-x(3-x)/(3-x)^2
=x^2/(3-x)^2
6.(x-2)-(x^2/x+2)=(x-2)(x+2)/(x+2)-(x^2/x+2)
=x^2-4-x^2/(x+2)
=-4/(x+2)
7.(2x/x^2-4)-(1/x-2)=2x/(x-2)(x+2)-(x+2)/(x-2)(x+2)
=(x-2)/(x-2)(x+2)
=1/(x+2)