$\frac{1}{8ab} = \frac{1 * a^2}{8ab * a^2} = \frac{a^2}{8a^3b}$
$\frac{1}{2a^3} = \frac{1 * 4b}{2a^3 * 4b} = \frac{4b}{8a^3b}$

$\frac{3x}{7m^3n^3} = \frac{3x * 3n}{7m^3n^3 * 3n} = \frac{9nx}{21m^3n^4}$
$\frac{4y}{3m^2n^4} = \frac{4y * 7m}{3m^2n^4 * 7m} = \frac{28my}{21m^3n^4}$

$\frac{a + b}{a - b} = \frac{(a + b) * (a + b)}{(a - b) * (a + b)} = \frac{(a + b)^2}{a^2 - b^2}$
$\frac{2}{a^2 - b^2}$

$\frac{3d}{m - n} = \frac{3d * (m - n)}{(m - n) * (m - n)} = \frac{3d(m - n)}{(m - n)^2}$
$\frac{8p}{(m - n)^2}$

$\frac{x}{2x + 1} = \frac{x(3x - 2)}{(2x + 1)(3x - 2)} = \frac{3x^2 - 2x}{6x^2 + 3x - 4x - 2} = \frac{3x^2 - 2x}{6x^2 - x - 2}$
$\frac{x}{3x - 2} = \frac{x(2x + 1)}{(3x - 2)(2x + 1)} = \frac{2x^2 + x}{6x^2 + 3x - 4x - 2} = \frac{2x^2 + x}{6x^2 - x - 2}$

$\frac{a - b}{3a + 3b} = \frac{a - b}{3(a + b)} = \frac{(a - b)(a - b)}{3(a + b)(a - b)} = \frac{(a - b)^2}{3(a^2 - b^2)}$
$\frac{a}{a^2 - b^2} = \frac{a}{(a - b)(a + b)} = \frac{3a}{3(a - b)(a + b)} = \frac{3a}{3(a^2 - b^2)}$

$\frac{3a}{4a - 4} = \frac{3a}{4(a - 1)} = \frac{5 * 3a}{5 * 4(a - 1)} = \frac{15a}{20(a - 1)}$
$\frac{2a}{5 - 5a} = \frac{2a}{5(1 - a)} = -\frac{4 * 2a}{4 * 5(a - 1)} = -\frac{8a}{20(a - 1)}$

$\frac{7a}{b - 3} = -\frac{7a}{3 - b} = -\frac{7a(3 + b)}{(3 - b)(3 + b)} = -\frac{7a(3 + b)}{9 - b^2}$
$\frac{c}{9 - b^2}$