17. (6分)已知$\frac{3x - 4}{(x - 1)(x - 2)}=\frac{A}{x - 1}+\frac{B}{x - 2}$,求实数$A$和$B$的值.

解：右边通分得：$\frac{A(x - 2) + B(x - 1)}{(x - 1)(x - 2)}$
分子展开：$A(x - 2) + B(x - 1) = (A + B)x - (2A + B)$
由等式两边分子相等得：$\begin{cases}A + B = 3 \\ - (2A + B) = -4\end{cases}$
解得：$\begin{cases}A = 1 \\ B = 2\end{cases}$
结论：$A = 1$，$B = 2$

18. (6分)先化简,再求值:$(\frac{3}{x + 1}-x + 1)÷\frac{x^{2}+4x + 4}{x + 1}$,其中$x = 3$.

化简过程：
$\begin{aligned}&\left(\frac{3}{x + 1} - x + 1\right)÷\frac{x^{2}+4x + 4}{x + 1}\\=&\left[\frac{3}{x + 1} - \frac{(x - 1)(x + 1)}{x + 1}\right] · \frac{x + 1}{(x + 2)^2}\\=&\frac{3 - (x^2 - 1)}{x + 1} · \frac{x + 1}{(x + 2)^2}\\=&\frac{4 - x^2}{x + 1} · \frac{x + 1}{(x + 2)^2}\\=&\frac{(2 - x)(2 + x)}{(x + 2)^2}\\=&\frac{2 - x}{x + 2}\end{aligned}$
求值过程：
当$x = 3$时，
$\frac{2 - 3}{3 + 2} = \frac{-1}{5} = -\frac{1}{5}$
答案：$-\frac{1}{5}$

化简过程：
$\begin{aligned}&\left(\frac{3}{x + 1} - x + 1\right)÷\frac{x^{2}+4x + 4}{x + 1}\\=&\left[\frac{3}{x + 1} - \frac{(x - 1)(x + 1)}{x + 1}\right] · \frac{x + 1}{(x + 2)^2}\\=&\frac{3 - (x^2 - 1)}{x + 1} · \frac{x + 1}{(x + 2)^2}\\=&\frac{4 - x^2}{x + 1} · \frac{x + 1}{(x + 2)^2}\\=&\frac{(2 - x)(2 + x)}{(x + 2)^2}\\=&\frac{2 - x}{x + 2}\end{aligned}$
求值过程：
当$x = 3$时，
$\frac{2 - 3}{3 + 2} = \frac{-1}{5} = -\frac{1}{5}$