化简：$\frac {x^{2}}{x-1}+\frac {x}{1-x}= $____.

$x$

1. 计算：
(1)$\frac {3x-y}{2x}+\frac {y}{2x}= $____； (2)(2024 湖北中考)$\frac {m}{m+1}+\frac {1}{m+1}= $____；
(3)$\frac {2a}{a-3}-\frac {6}{a-3}= $____； (4)(2024 威海)$\frac {4}{x-2}+\frac {x^{2}}{2-x}= $____.

(1)$\frac{3}{2}$ (2)1 (3)2 (4)$-x - 2$

2. (教材变式)计算：
(1)$\frac {a^{2}+2}{a+1}-\frac {3}{1+a}$； (2)$\frac {a}{a^{2}-1}+\frac {3a+1}{a^{2}-1}+\frac {2a+3}{1-a^{2}}$.

解：(1)原式$=\frac{a^{2}+2 - 3}{a + 1}$
$=\frac{(a + 1)(a - 1)}{a + 1}$
$=a - 1$；
(2)原式$=\frac{a + 3a + 1 - 2a - 3}{a^{2} - 1}$
$=\frac{2a - 2}{a^{2} - 1}=\frac{2(a - 1)}{(a + 1)(a - 1)}$
$=\frac{2}{a + 1}$．

3. 计算：(1)$\frac {x+2}{2x}-\frac {1}{x}= $____； (2)$\frac {1}{6x}+\frac {2}{9x^{2}}= $____；
(3)$\frac {1}{a-3}-\frac {3}{a(a-3)}= $____； (4)$\frac {x^{2}+x}{x}+x-1= $____；
(5)(2024 西宁)$\frac {2a}{a^{2}-b^{2}}-\frac {1}{a+b}= $____； (6)$\frac {x^{2}-9}{x^{2}+6x+9}-\frac {2x+1}{2x+6}= $____.

(1)$\frac{1}{2}$ (2)$\frac{3x + 4}{18x^{2}}$ (3)$\frac{1}{a}$
(4)$2x$ (5)$\frac{1}{a - b}$ (6)$-\frac{7}{2(x + 3)}$

4. (教材变式)计算：
(1)$\frac {3}{2mn}+\frac {2}{3m^{2}n}+\frac {1}{4mn^{2}}$； (2)$\frac {1}{a^{2}-a}+\frac {a-3}{a^{2}-1}$.

解：(1)原式$=\frac{18mn}{12m^{2}n^{2}}+\frac{8n}{12m^{2}n^{2}}+$
$\frac{3m}{12m^{2}n^{2}}$
$=\frac{18mn + 8n + 3m}{12m^{2}n^{2}}$；
(2)原式$=\frac{1}{a(a - 1)}+\frac{a - 3}{(a + 1)(a - 1)}$
$=\frac{a + 1}{a(a + 1)(a - 1)}+$
$\frac{a(a - 3)}{a(a + 1)(a - 1)}$
$=\frac{a^{2} - 2a + 1}{a(a + 1)(a - 1)}$
$=\frac{(a - 1)^{2}}{a(a + 1)(a - 1)}$
$=\frac{a - 1}{a(a + 1)}$．