$\frac{a + 7}{12} + \frac{a - 4}{9} = \frac{3(a + 7) + 4(a - 4)}{36} = \frac{3a + 21 + 4a - 16}{36} = \frac{7a + 5}{36}$

$\frac{2b - 7c}{6} - \frac{3b + 2c}{15} = \frac{5(2b - 7c) - 2(3b + 2c)}{30} = \frac{10b - 35c - 6b - 4c}{30} = \frac{4b - 39c}{30}$

$\frac{3x - 2}{x} - \frac{3y - 1}{y} = \frac{y(3x - 2) - x(3y - 1)}{xy} = \frac{3xy - 2y - 3xy + x}{xy} = \frac{x - 2y}{xy}$

$\frac{6p + 1}{p} - \frac{2p + 8}{3p} = \frac{3(6p + 1) - (2p + 8)}{3p} = \frac{18p + 3 - 2p - 8}{3p} = \frac{16p - 5}{3p}$

$\frac{5m - n}{14m} - \frac{m - 6n}{7m} = \frac{5m - n - 2(m - 6n)}{14m} = \frac{5m - n - 2m + 12n}{14m} = \frac{3m + 11n}{14m}$

$\frac{x + 4}{11x} - \frac{y - 3}{11y} = \frac{y(x + 4) - x(y - 3)}{11xy} = \frac{xy + 4y - xy + 3x}{11xy} = \frac{4y + 3x}{11xy}$

$\frac{a + b}{ab} + \frac{a - c}{ac} = \frac{c(a + b) + b(a - c)}{abc} = \frac{ac + bc + ab - bc}{abc} = \frac{ac + ab}{abc} = \frac{a(b + c)}{abc} = \frac{b + c}{bc}$

$\frac{2}{p^2} + \frac{p - 1}{p} = \frac{2 + p(p - 1)}{p^2} = \frac{p^2 - p + 2}{p^2}$

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

$\frac{x - y}{x^3} - \frac{y - x^2}{x^2y} = \frac{y(x - y) - x(y - x^2)}{x^3y} = \frac{xy - y^2 - xy + x^3}{x^3y} = \frac{x^3 - y^2}{x^3y}$

$\frac{2m - 3n}{m^2n} + \frac{7m - 2n}{mn^2} = \frac{n(2m - 3n) + m(7m - 2n)}{m^2n^2} = \frac{2mn - 3n^2 + 7m^2 - 2mn}{m^2n^2} = \frac{7m^2 - 3n^2}{m^2n^2}$

$\frac{c + d}{cd^4} - \frac{c^2 - 8d}{c^3d^3} = \frac{c^2(c + d) - d(c^2 - 8d)}{c^3d^4} = \frac{c^3 + c^2d - c^2d + 8d^2}{c^3d^4} = \frac{c^3 + 8d^2}{c^3d^4}$