1. 分式$\frac{1}{2x^{2}y}$与$\frac{1}{6xy^{2}}$的最简公分母是.

$6x^2y^2$

2. 将分式$\frac{4a}{5b^{2}c},\frac{3c}{10a^{2}b},\frac{5b}{-2ac^{2}}$通分时，分子、分母依次同乘，，.

$2a^2c$
$bc^2$
$-5ab^2$

3. 把分式$\frac{a - b}{a^{2} + 2ab + b^{2}},\frac{b}{a^{2} - b^{2}},\frac{1}{a^{2} - 2ab + b^{2}}$通分后，其分子分别是()

A.$(a - b)^{3},b(a + b)(a - b),(a + b)^{2}$
B.$(a + b)^{2}(a - b)^{3},b(a + b)(a - b),(a - b)^{2}$
C.$(a + b)^{2}(a - b)^{2},(a + b)(a - b),(a + b)^{2}$
D.$(a - b)^{3},b(a + b)(a - b),(a - b)^{2}$

A

4. 分式$\frac{3a}{a^{2} - b^{2}}$的分母经过通分后变成$2(a - b)^{2}(a + b)$，分子应变为()

A.$6a(a - b)^{2}(a + b)$
B.$2(a - b)$
C.$6a(a - b)$
D.$6a(a + b)$

C

5. 通分：

(1)$\frac{2}{3a - 9},\frac{a - 1}{a^{2} - 9}$；
(2)$\frac{m}{m + n},\frac{1}{m^{2}n - mn^{2}}$；
(3)$\frac{2}{a^{2} + 2a + 1},\frac{a}{a^{2} - 1}$；
(4)$\frac{2}{9 - 4m^{2}},\frac{3m}{4m^{2} - 12m + 9}$；
(5)$-\frac{1}{8x^{4}y},\frac{2}{3x^{2}y^{3}z},\frac{5}{6xz^{2}}$；
(6)$\frac{1}{x - 2},\frac{1}{(x - 2)(x + 3)},\frac{2}{(x + 3)^{2}}$.

解：$​\frac {2}{3a-9}= \frac {2(a+3)}{3(a-3)(a+3)}$，
$​​\frac {a-1}{a²-9}=\frac {3(a-1)}{3(a-3)(a+3)}​$
解：$​\frac {m}{m+n}= \frac {\mathrm {m^2}n(m-n)}{mn(m+n)(m-n)}$，​
$​\frac {1}{m²n-mn²}=\frac {m+n}{mn(m+n)(m-n)}​$
解：$​\frac {2}{a²+2a+1}= \frac {2(a-1)}{(a+1)^2(a-1)}$，​​
$\frac {a}{a²-1}=\frac {a(a+1)}{(a+1)^2(a-1)}​$
解：$​\frac {2}{9-4m²}= \frac {2(3-2m)}{(3-2m)^2(3+2m)}$，
$​​\frac {3m}{4m²-12m+9}\frac {3m(3+2m)}{(3-2m)^2(3+2m)}​$
解：$​-\frac {1}{8x^4y} =-\frac {3y^2z^2}{24x^4y^3z^2}$，​
$​\frac {2}{3x²y^3z}=\frac {16x^2z}{24x^4y^3z^2}$，​
$​\frac {5}{6xz²}=\frac {20x^3y^3}{24x^4y^3z^2}​$
解：$​\frac {1}{x-2}= \frac {(x+3)^2}{(x-2)(x+3)^2}$，​
$​\frac {1}{(x-2)(x+3)}=\frac {x+3}{(x-2)(x+3)^2}$，​
$​\frac {2}{(x+3)²}=\frac {2(x-2)}{(x-2)(x+3)^2}​$