计算:
(1)$\frac {3}{a}+\frac {a-15}{5a}$; (2)$\frac {1}{x+2}-\frac {2x}{x^{2}-4}$;
(3)$\frac {2a}{a^{2}-4}-\frac {1}{a-2}$; (4)$\frac {2x}{x+2}-\frac {x^{2}-4x+4}{x^{2}-4}$;
(5)$\frac {a}{a-1}+\frac {3a-1}{1-a^{2}}$; (6)$\frac {x-1}{x^{2}-2x+1}+\frac {x}{1-x}$;
(7)$x+3-\frac {x^{2}}{x-2}$; (8)$\frac {1}{1+x}+x-1$;
(9)$\frac {x^{2}}{x+3}-x+3$; (10)$\frac {2}{x+2}+\frac {2}{x-2}-\frac {x^{2}+4}{x^{2}-4}$.
答案：(1)解：原式$=\frac{15}{5a}+\frac{a-15}{5a}=\frac{15+a-15}{5a}=\frac{a}{5a}=\frac{1}{5}$
(2)解：原式$=\frac{1}{x+2}-\frac{2x}{(x+2)(x-2)}=\frac{x-2}{(x+2)(x-2)}-\frac{2x}{(x+2)(x-2)}=\frac{x-2-2x}{(x+2)(x-2)}=\frac{-x-2}{(x+2)(x-2)}=-\frac{x+2}{(x+2)(x-2)}=-\frac{1}{x-2}$
(3)解：原式$=\frac{2a}{(a+2)(a-2)}-\frac{a+2}{(a+2)(a-2)}=\frac{2a-(a+2)}{(a+2)(a-2)}=\frac{2a-a-2}{(a+2)(a-2)}=\frac{a-2}{(a+2)(a-2)}=\frac{1}{a+2}$
(4)解：原式$=\frac{2x}{x+2}-\frac{(x-2)^2}{(x+2)(x-2)}=\frac{2x}{x+2}-\frac{x-2}{x+2}=\frac{2x-(x-2)}{x+2}=\frac{2x-x+2}{x+2}=\frac{x+2}{x+2}=1$
(5)解：原式$=\frac{a}{a-1}-\frac{3a-1}{(a+1)(a-1)}=\frac{a(a+1)}{(a+1)(a-1)}-\frac{3a-1}{(a+1)(a-1)}=\frac{a^2+a-3a+1}{(a+1)(a-1)}=\frac{a^2-2a+1}{(a+1)(a-1)}=\frac{(a-1)^2}{(a+1)(a-1)}=\frac{a-1}{a+1}$
(6)解：原式$=\frac{x-1}{(x-1)^2}-\frac{x}{x-1}=\frac{1}{x-1}-\frac{x}{x-1}=\frac{1-x}{x-1}=-\frac{x-1}{x-1}=-1$
(7)解：原式$=\frac{(x+3)(x-2)}{x-2}-\frac{x^2}{x-2}=\frac{x^2-2x+3x-6-x^2}{x-2}=\frac{x-6}{x-2}$
(8)解：原式$=\frac{1}{x+1}+\frac{(x-1)(x+1)}{x+1}=\frac{1+x^2-1}{x+1}=\frac{x^2}{x+1}$
(9)解：原式$=\frac{x^2}{x+3}-\frac{(x-3)(x+3)}{x+3}=\frac{x^2-(x^2-9)}{x+3}=\frac{x^2-x^2+9}{x+3}=\frac{9}{x+3}$
(10)解：原式$=\frac{2(x-2)}{(x+2)(x-2)}+\frac{2(x+2)}{(x+2)(x-2)}-\frac{x^2+4}{(x+2)(x-2)}=\frac{2x-4+2x+4-x^2-4}{(x+2)(x-2)}=\frac{-x^2+4x-4}{(x+2)(x-2)}=\frac{-(x^2-4x+4)}{(x+2)(x-2)}=\frac{-(x-2)^2}{(x+2)(x-2)}=-\frac{x-2}{x+2}$
