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18. 计算:
(1) $\frac{1}{a-1} - \frac{2}{1-a^2}$;
(2) $(ab - b^2) ÷ \frac{a^2 - b^2}{a + b}$;
(3) $(2a + 3b)(2a - b)$;
(4) $[x(x^2y^2 - xy) - y(x^2 - x^3y)] ÷ 3x^2y$.
(1) $\frac{1}{a-1} - \frac{2}{1-a^2}$;
(2) $(ab - b^2) ÷ \frac{a^2 - b^2}{a + b}$;
(3) $(2a + 3b)(2a - b)$;
(4) $[x(x^2y^2 - xy) - y(x^2 - x^3y)] ÷ 3x^2y$.
答案
18. (1) $\frac{a+3}{a^2-1}$ (2) $b$ (3) $4a^2+4ab-3b^2$
(4) $\frac{2}{3}xy-\frac{2}{3}$
(4) $\frac{2}{3}xy-\frac{2}{3}$
19. 分解因式:
(1) $-3x^2+6xy-3y^2$;
(2) $a^2(x-y)+16(y-x)$.
(1) $-3x^2+6xy-3y^2$;
(2) $a^2(x-y)+16(y-x)$.
答案
19. (1) $-3(x-y)^2$ (2) $(x-y)(a+4)(a-4)$
20. 解下列方程:
(1) $\frac{5x+2}{x^2+x}=\frac{3}{x+1}$;
(2) $\frac{2x}{2x-5}-\frac{2}{2x+5}=1$.
(1) $\frac{5x+2}{x^2+x}=\frac{3}{x+1}$;
(2) $\frac{2x}{2x-5}-\frac{2}{2x+5}=1$.
答案
20. (1) 原分式方程无解 (2) $x=-\frac{35}{6}$
21. 如图8，在$△ ABC$中，$∠ C=90°$，D为BC边上一点，$DE ⊥ AB$于点E，F为AC边上一点，且$BD=FD$，$CF=BE$. 求证：AD是$∠ BAC$的平分线.
答案
21. 提示:在$Rt△DCF$和$Rt△DEB$中,$\begin{cases}BD=FD,\\CF=BE,\end{cases}$
$\therefore Rt△DCF≌ Rt△DEB. \therefore CD=ED.$
$\therefore AD$是$∠BAC$的平分线.
$\therefore Rt△DCF≌ Rt△DEB. \therefore CD=ED.$
$\therefore AD$是$∠BAC$的平分线.
