$\frac{7y}{y^2 - 4} - \frac{14}{y^2 - 4} = \frac{7y - 14}{y^2 - 4} = \frac{7(y - 2)}{(y - 2)(y + 2)} = \frac{7}{y + 2}$

$\frac{y^2 - 3y}{25 - y^2} - \frac{7y - 25}{25 - y^2} = \frac{y^2 - 3y - (7y - 25)}{25 - y^2} = \frac{y^2 - 3y - 7y + 25}{25 - y^2} = \frac{y^2 - 10y + 25}{25 - y^2} = \frac{(y - 5)^2}{(5 - y)(5 + y)} = \frac{(5 - y)^2}{(5 - y)(5 + y)} = \frac{5 - y}{5 + y}$

$\frac{9p + 5}{3p + 6} - \frac{10p - 12}{3p + 6} + \frac{9p - 1}{3p + 6} = \frac{9p + 5 - (10p - 12) + 9p - 1}{3p + 6} = \frac{9p + 5 - 10p + 12 + 9p - 1}{3p + 6} = \frac{8p + 16}{3p + 6} = \frac{8(p + 2)}{3(p + 2)} = \frac{8}{3} = 2\frac{2}{3}$

$\frac{7x + 5}{3 - x} + \frac{5x + 11}{x - 3} = \frac{7x + 5}{3 - x} - \frac{5x + 11}{3 - x} = \frac{7x + 5 - (5x + 11)}{3 - x} = \frac{7x + 5 - 5x - 11}{3 - x} = \frac{2x - 6}{3 - x} = \frac{2(x - 3)}{3 - x} = -\frac{2(x - 3)}{x - 3} = -2$

$\frac{(3a - 1)^2}{4a - 4} + \frac{(a - 3)^2}{4 - 4a} = \frac{(3a - 1)^2}{4a - 4} - \frac{(a - 3)^2}{4a - 4} = \frac{(3a - 1)^2 - (a - 3)^2}{4a - 4} = \frac{9a^2 - 6a + 1 - (a^2 - 6a + 9)}{4a - 4} = \frac{9a^2 - 6a + 1 - a^2 + 6a - 9}{4a - 4} = \frac{8a^2 - 8}{4a - 4} = \frac{8(a^2 - 1)}{4(a - 1)} = \frac{8(a - 1)(a + 1)}{4(a - 1)} = 2(a + 1)$

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

$\frac{7}{a - 2} - \frac{b}{2 - a} = \frac{7}{a - 2} + \frac{b}{a - 2} = \frac{7 + b}{a - 2}$

$\frac{6a}{5 - a} - \frac{4a}{a - 5} = \frac{6a}{5 - a} + \frac{4a}{5 - a} = \frac{6a + 4a}{5 - a} = \frac{10a}{5 - a}$