Ты просишь меня упростить алгебраические выражения, содержащие дроби с переменными.

Выполню вычисления по порядку для каждого выражения: a) $\frac{3a}{a+b} + \frac{3b}{a+b} = \frac{3a + 3b}{a+b} = \frac{3(a+b)}{a+b} = 3$ b) $\frac{\alpha}{\alpha - 3} + \frac{3}{3 - \alpha} = \frac{\alpha}{\alpha - 3} - \frac{3}{\alpha - 3} = \frac{\alpha - 3}{\alpha - 3} = 1$ c) $\frac{3x}{x - 2y} - \frac{6y}{x - 2y} = \frac{3x - 6y}{x - 2y} = \frac{3(x - 2y)}{x - 2y} = 3$ d) $\frac{12\alpha}{3a+b} + \frac{4b}{3\alpha + b}$ – здесь нужно привести к общему знаменателю: $\frac{12\alpha}{3a+b} + \frac{4b}{3\alpha + b} = \frac{12\alpha(3\alpha + b) + 4b(3a+b)}{(3a+b)(3\alpha + b)} = \frac{36\alpha^2 + 12\alpha b + 12ab + 4b^2}{(3a+b)(3\alpha + b)}$ e) $\frac{14m}{2m-n} + \frac{7n}{n - 2m} = \frac{14m}{2m-n} - \frac{7n}{2m - n} = \frac{14m - 7n}{2m - n} = \frac{7(2m - n)}{2m - n} = 7$ f) $\frac{21m}{3m + n} + \frac{7n}{n + 3m} = \frac{21m + 7n}{3m + n} = \frac{7(3m + n)}{3m + n} = 7$ g) $\frac{ax^2}{a-m} - \frac{mx^2}{a-m} = \frac{ax^2 - mx^2}{a-m} = \frac{x^2(a - m)}{a - m} = x^2$ h) $\frac{7x}{x^2+5} + \frac{x^3-2x}{x^2+5} = \frac{7x + x^3 - 2x}{x^2 + 5} = \frac{x^3 + 5x}{x^2 + 5} = \frac{x(x^2 + 5)}{x^2 + 5} = x$ i) $\frac{8x^2}{x^2+1} - \frac{5x^2-3}{x^2+1} = \frac{8x^2 - (5x^2 - 3)}{x^2 + 1} = \frac{8x^2 - 5x^2 + 3}{x^2 + 1} = \frac{3x^2 + 3}{x^2 + 1} = \frac{3(x^2 + 1)}{x^2 + 1} = 3$ j) $\frac{7x-2}{x+2} - \frac{3x-10}{x+2} = \frac{(7x - 2) - (3x - 10)}{x + 2} = \frac{7x - 2 - 3x + 10}{x + 2} = \frac{4x + 8}{x + 2} = \frac{4(x + 2)}{x + 2} = 4$ k) $\frac{15}{c^2-5c} - \frac{3c}{c^2-5c} = \frac{15 - 3c}{c^2 - 5c} = \frac{3(5 - c)}{c(c - 5)} = -\frac{3}{c}$ l) $\frac{22m+k}{15m + 5k} + \frac{8m+9k}{5k + 15m} = \frac{22m + k}{15m + 5k} + \frac{8m + 9k}{15m + 5k} = \frac{22m + k + 8m + 9k}{15m + 5k} = \frac{30m + 10k}{15m + 5k} = \frac{10(3m + k)}{5(3m + k)} = 2$ m) $\frac{17x-4\alpha}{x-\alpha} + \frac{6x+7\alpha}{\alpha-x} = \frac{17x - 4\alpha}{x - \alpha} - \frac{6x + 7\alpha}{x - \alpha} = \frac{17x - 4\alpha - 6x - 7\alpha}{x - \alpha} = \frac{11x - 11\alpha}{x - \alpha} = \frac{11(x - \alpha)}{x - \alpha} = 11$ n) $\frac{2m}{m-n} + \frac{2n}{n-m} = \frac{2m}{m - n} - \frac{2n}{m - n} = \frac{2m - 2n}{m - n} = \frac{2(m - n)}{m - n} = 2$ o) $\frac{2a+b}{a-b} + \frac{2b-5a}{a-b} = \frac{2a + b + 2b - 5a}{a - b} = \frac{-3a + 3b}{a - b} = \frac{3(b - a)}{a - b} = -3$