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一、选择题
1. 下列分式计算正确的是(
A.$\frac{a}{b}·\frac{c}{d}=\frac{ad}{bc}$
B.$\frac{m^{4}}{n^{5}}·\frac{n^{4}}{m^{3}}=\frac{m}{n}$
C.$(\frac{2a}{a - b})^{2}=\frac{4a^{2}}{a^{2}-b^{2}}$
D.$(\frac{3x}{4y})^{3}=\frac{3x^{3}}{4y^{3}}$
1. 下列分式计算正确的是(
B
)A.$\frac{a}{b}·\frac{c}{d}=\frac{ad}{bc}$
B.$\frac{m^{4}}{n^{5}}·\frac{n^{4}}{m^{3}}=\frac{m}{n}$
C.$(\frac{2a}{a - b})^{2}=\frac{4a^{2}}{a^{2}-b^{2}}$
D.$(\frac{3x}{4y})^{3}=\frac{3x^{3}}{4y^{3}}$
答案
1. B
2. 计算$\frac{a - b}{a + b}÷(b - a)$的结果是(
A.$\frac{1}{a + b}$
B.$-\frac{1}{a + b}$
C.$\frac{1}{-a + b}$
D.$\frac{1}{a - b}$
B
)A.$\frac{1}{a + b}$
B.$-\frac{1}{a + b}$
C.$\frac{1}{-a + b}$
D.$\frac{1}{a - b}$
答案
2. B
解析
$\begin{aligned}\frac{a - b}{a + b}÷(b - a)&=\frac{a - b}{a + b}×\frac{1}{b - a}\\&=\frac{-(b - a)}{a + b}×\frac{1}{b - a}\\&=-\frac{1}{a + b}\end{aligned}$
B
B
二、填空题
3. $(a - b)÷\frac{a^{2}-b^{2}}{a + b}·(a + b)=$
3. $(a - b)÷\frac{a^{2}-b^{2}}{a + b}·(a + b)=$
$ a + b $
答案
3. $ a + b $
解析
$(a - b)÷\frac{a^{2}-b^{2}}{a + b}·(a + b)$
$=(a - b)·\frac{a + b}{(a + b)(a - b)}·(a + b)$
$=(a - b)·\frac{1}{a - b}·(a + b)$
$=1·(a + b)$
$=a + b$
$=(a - b)·\frac{a + b}{(a + b)(a - b)}·(a + b)$
$=(a - b)·\frac{1}{a - b}·(a + b)$
$=1·(a + b)$
$=a + b$
4. $\frac{2a}{3b}·\frac{9b^{2}}{8a^{2}}=$
$ \frac{3b}{4a} $
答案
4. $ \frac{3b}{4a} $
解析
$\frac{2a}{3b}·\frac{9b^{2}}{8a^{2}}=\frac{2a·9b^{2}}{3b·8a^{2}}=\frac{18ab^{2}}{24a^{2}b}=\frac{3b}{4a}$
5. $2a÷\frac{a}{b}·\frac{b}{2a}=$
$ \frac{b^{2}}{a} $
答案
5. $ \frac{b^{2}}{a} $
解析
$2a÷\frac{a}{b}·\frac{b}{2a}$
$=2a·\frac{b}{a}·\frac{b}{2a}$
$=2b·\frac{b}{2a}$
$=\frac{2b^2}{2a}$
$=\frac{b^2}{a}$
$=2a·\frac{b}{a}·\frac{b}{2a}$
$=2b·\frac{b}{2a}$
$=\frac{2b^2}{2a}$
$=\frac{b^2}{a}$
6. $\frac{2x + 2y}{5a^{2}b}·\frac{10ab^{2}}{x^{2}-y^{2}}=$
$ \frac{4b}{ax - ay} $
答案
6. $ \frac{4b}{ax - ay} $
解析
$\frac{2x + 2y}{5a^{2}b}·\frac{10ab^{2}}{x^{2}-y^{2}}$
$=\frac{2(x + y)}{5a^{2}b}·\frac{10ab^{2}}{(x + y)(x - y)}$
$=\frac{2×10ab^{2}(x + y)}{5a^{2}b(x + y)(x - y)}$
$=\frac{20ab^{2}}{5a^{2}b(x - y)}$
$=\frac{4b}{a(x - y)}$
$=\frac{4b}{ax - ay}$
$=\frac{2(x + y)}{5a^{2}b}·\frac{10ab^{2}}{(x + y)(x - y)}$
$=\frac{2×10ab^{2}(x + y)}{5a^{2}b(x + y)(x - y)}$
$=\frac{20ab^{2}}{5a^{2}b(x - y)}$
$=\frac{4b}{a(x - y)}$
$=\frac{4b}{ax - ay}$
三、解答题
7. 计算：
(1) $\frac{x^{2}y}{x^{3}}·(-\frac{1}{y})$
(2) $\frac{12xy}{5y}÷(-8x^{2}y)$
(3) $\frac{a^{2}-1}{a^{2}+2a + 1}÷\frac{a^{2}-a}{a + 1}$
(4) $\frac{4}{a^{2}-1}·\frac{a - 1}{6a}$
7. 计算：
(1) $\frac{x^{2}y}{x^{3}}·(-\frac{1}{y})$
(2) $\frac{12xy}{5y}÷(-8x^{2}y)$
(3) $\frac{a^{2}-1}{a^{2}+2a + 1}÷\frac{a^{2}-a}{a + 1}$
(4) $\frac{4}{a^{2}-1}·\frac{a - 1}{6a}$
答案
7. (1) $ -\frac{1}{x} $ (2) $ -\frac{3}{10xy} $ (3) $ \frac{1}{a} $ (4) $ \frac{2}{3a^{2} + 3a} $
解析
(1) $\frac{x^{2}y}{x^{3}}·(-\frac{1}{y})=\frac{y}{x}·(-\frac{1}{y})=-\frac{1}{x}$
(2) $\frac{12xy}{5y}÷(-8x^{2}y)=\frac{12x}{5}·(-\frac{1}{8x^{2}y})=-\frac{3}{10xy}$
(3) $\frac{a^{2}-1}{a^{2}+2a + 1}÷\frac{a^{2}-a}{a + 1}=\frac{(a+1)(a-1)}{(a+1)^{2}}·\frac{a+1}{a(a-1)}=\frac{1}{a}$
(4) $\frac{4}{a^{2}-1}·\frac{a - 1}{6a}=\frac{4}{(a+1)(a-1)}·\frac{a - 1}{6a}=\frac{2}{3a(a+1)}=\frac{2}{3a^{2}+3a}$
(2) $\frac{12xy}{5y}÷(-8x^{2}y)=\frac{12x}{5}·(-\frac{1}{8x^{2}y})=-\frac{3}{10xy}$
(3) $\frac{a^{2}-1}{a^{2}+2a + 1}÷\frac{a^{2}-a}{a + 1}=\frac{(a+1)(a-1)}{(a+1)^{2}}·\frac{a+1}{a(a-1)}=\frac{1}{a}$
(4) $\frac{4}{a^{2}-1}·\frac{a - 1}{6a}=\frac{4}{(a+1)(a-1)}·\frac{a - 1}{6a}=\frac{2}{3a(a+1)}=\frac{2}{3a^{2}+3a}$
