计算:
(1)$\frac {2-x}{x^{2}-4}+\frac {2x+4}{x^{2}+4x+4};$ (2)$\frac {-2}{a-1}+\frac {a^{2}-4a+4}{a^{2}-1}\cdot \frac {a+1}{a-2};$
(3)$(\frac {3}{x-2}+\frac {2}{x+2})÷\frac {5x^{2}+2x}{x^{2}-4};$ (4)$\frac {1}{x}-\frac {x^{2}-1}{x+1}\cdot \frac {1}{x^{2}-2x+1};$
(5)$(\frac {1}{x-1}+\frac {1}{x+1})+\frac {x+2}{x^{2}-1};$ (6)$\frac {x-2}{x^{2}+x}÷\frac {x^{2}-4x+4}{x+1}+\frac {1}{x};$
(7)$(1-\frac {1}{x+1})÷\frac {1}{x^{2}-1}+x-2;$ (8)$(1+\frac {1}{x-2})÷\frac {x^{2}-2x+1}{x^{2}-4}.$
答案：(1)解：原式$=\frac{-(x-2)}{(x+2)(x-2)}+\frac{2(x+2)}{(x+2)^2}=-\frac{1}{x+2}+\frac{2}{x+2}=\frac{1}{x+2}$
(2)解：原式$=\frac{-2}{a-1}+\frac{(a-2)^2}{(a+1)(a-1)}\cdot\frac{a+1}{a-2}=\frac{-2}{a-1}+\frac{a-2}{a-1}=\frac{a-4}{a-1}$
(3)解：原式$=\frac{3(x+2)+2(x-2)}{(x+2)(x-2)}\cdot\frac{(x+2)(x-2)}{x(5x+2)}=\frac{5x+2}{(x+2)(x-2)}\cdot\frac{(x+2)(x-2)}{x(5x+2)}=\frac{1}{x}$
(4)解：原式$=\frac{1}{x}-\frac{(x+1)(x-1)}{x+1}\cdot\frac{1}{(x-1)^2}=\frac{1}{x}-\frac{1}{x-1}=\frac{x-1-x}{x(x-1)}=\frac{-1}{x(x-1)}=\frac{1}{x-x^2}$
(5)解：原式$=\frac{x+1+x-1}{(x+1)(x-1)}+\frac{x+2}{x^2-1}=\frac{2x}{x^2-1}+\frac{x+2}{x^2-1}=\frac{3x+2}{x^2-1}$
(6)解：原式$=\frac{x-2}{x(x+1)}\cdot\frac{x+1}{(x-2)^2}+\frac{1}{x}=\frac{1}{x(x-2)}+\frac{1}{x}=\frac{1+x-2}{x(x-2)}=\frac{x-1}{x^2-2x}$
(7)解：原式$=\frac{x+1-1}{x+1}\cdot(x+1)(x-1)+x-2=x(x-1)+x-2=x^2-x+x-2=x^2-2$
(8)解：原式$=\frac{x-2+1}{x-2}\cdot\frac{(x+2)(x-2)}{(x-1)^2}=\frac{x-1}{x-2}\cdot\frac{(x+2)(x-2)}{(x-1)^2}=\frac{x+2}{x-1}$
