计算:
(1)$\frac {2a^{2}-3}{a+1}-\frac {a^{2}-2}{a+1}$; (2)$\frac {x^{2}-4x}{x-3}-\frac {2x-9}{x-3}$;
(3)$\frac {3a}{a-b}-\frac {3b}{a-b}$; (4)$\frac {a+3}{a^{2}+2a}-\frac {1}{2a+a^{2}}$;
(5)$\frac {3m-n}{(m-n)^{2}}-\frac {m+n}{(n-m)^{2}}$; (6)$\frac {a}{a-b}+\frac {b}{b-a}$;
(7)$\frac {a^{2}}{a-1}+\frac {1}{1-a}$; (8)$\frac {m}{m-n}-\frac {n}{m+n}+\frac {2mn}{m^{2}-n^{2}}$;
(9)$\frac {5a+6b}{3a^{2}bc}+\frac {3b-4a}{3ba^{2}c}-\frac {a+3b}{3cba^{2}}$; (10)$\frac {3b+a}{a^{2}-b^{2}}-\frac {a+2b}{a^{2}-b^{2}}-\frac {3a-4b}{b^{2}-a^{2}}$.
答案：(1)解：原式$=\frac{(2a^{2}-3)-(a^{2}-2)}{a+1}=\frac{2a^{2}-3-a^{2}+2}{a+1}=\frac{a^{2}-1}{a+1}=\frac{(a+1)(a-1)}{a+1}=a-1$
(2)解：原式$=\frac{(x^{2}-4x)-(2x-9)}{x-3}=\frac{x^{2}-4x-2x+9}{x-3}=\frac{x^{2}-6x+9}{x-3}=\frac{(x-3)^{2}}{x-3}=x-3$
(3)解：原式$=\frac{3a-3b}{a-b}=\frac{3(a-b)}{a-b}=3$
(4)解：原式$=\frac{(a+3)-1}{a^{2}+2a}=\frac{a+2}{a(a+2)}=\frac{1}{a}$
(5)解：原式$=\frac{3m-n}{(m-n)^{2}}-\frac{m+n}{(m-n)^{2}}=\frac{(3m-n)-(m+n)}{(m-n)^{2}}=\frac{3m-n-m-n}{(m-n)^{2}}=\frac{2m-2n}{(m-n)^{2}}=\frac{2(m-n)}{(m-n)^{2}}=\frac{2}{m-n}$
(6)解：原式$=\frac{a}{a-b}-\frac{b}{a-b}=\frac{a-b}{a-b}=1$
(7)解：原式$=\frac{a^{2}}{a-1}-\frac{1}{a-1}=\frac{a^{2}-1}{a-1}=\frac{(a+1)(a-1)}{a-1}=a+1$
(8)解：原式$=\frac{m(m+n)}{(m-n)(m+n)}-\frac{n(m-n)}{(m-n)(m+n)}+\frac{2mn}{(m-n)(m+n)}=\frac{m(m+n)-n(m-n)+2mn}{(m-n)(m+n)}=\frac{m^{2}+mn - mn + n^{2}+2mn}{(m-n)(m+n)}=\frac{m^{2}+2mn + n^{2}}{(m-n)(m+n)}=\frac{(m + n)^{2}}{(m - n)(m + n)}=\frac{m + n}{m - n}$
(9)解：原式$=\frac{(5a + 6b)+(3b - 4a)-(a + 3b)}{3a^{2}bc}=\frac{5a + 6b + 3b - 4a - a - 3b}{3a^{2}bc}=\frac{6b}{3a^{2}bc}=\frac{2}{a^{2}c}$
(10)解：原式$=\frac{3b + a}{a^{2}-b^{2}}-\frac{a + 2b}{a^{2}-b^{2}}+\frac{3a - 4b}{a^{2}-b^{2}}=\frac{(3b + a)-(a + 2b)+(3a - 4b)}{a^{2}-b^{2}}=\frac{3b + a - a - 2b + 3a - 4b}{a^{2}-b^{2}}=\frac{3a - 3b}{a^{2}-b^{2}}=\frac{3(a - b)}{(a + b)(a - b)}=\frac{3}{a + b}$
