Вопрос:

Помоги решить примеры на сложение и вычитание алгебраических дробей

Фотография

Ответ ассистента

a) $$\frac{3a}{a+b} + \frac{3b}{a+b} = \frac{3a+3b}{a+b} = \frac{3(a+b)}{a+b} = 3$$ б) $$\frac{\alpha}{\alpha - 3} + \frac{3}{3 - \alpha} = \frac{\alpha}{\alpha - 3} - \frac{3}{\alpha - 3} = \frac{\alpha - 3}{\alpha - 3} = 1$$ в) $$\frac{3x}{x - 2y} - \frac{6y}{x - 2y} = \frac{3x - 6y}{x - 2y} = \frac{3(x - 2y)}{x - 2y} = 3$$ г) $$\frac{12\alpha}{3a+b} + \frac{4b}{3\alpha+b} = \frac{12\alpha + 4b}{3a+b} = \frac{4(3\alpha + b)}{3a+b} = 4$$ д) $$\frac{14m}{2m-n} + \frac{7n}{n - 2m} = \frac{14m}{2m-n} - \frac{7n}{2m - n} = \frac{14m - 7n}{2m - n} = \frac{7(2m - n)}{2m - n} = 7$$ е) $$\frac{21m}{3m + n} + \frac{7n}{n + 3m} = \frac{21m + 7n}{3m + n} = \frac{7(3m + n)}{3m + n} = 7$$ ж) $$\frac{ax^2}{a-m} - \frac{mx^2}{a-m} = \frac{ax^2 - mx^2}{a-m} = \frac{x^2(a - m)}{a-m} = x^2$$ з) $$\frac{7x}{x^2+5} + \frac{x^3-2x}{x^2+5} = \frac{7x + x^3 - 2x}{x^2+5} = \frac{x^3 + 5x}{x^2+5} = \frac{x(x^2 + 5)}{x^2+5} = x$$ и) $$\frac{8x^2}{x^2+1} - \frac{5x^2-3}{x^2+1} = \frac{8x^2 - 5x^2 + 3}{x^2+1} = \frac{3x^2 + 3}{x^2+1} = \frac{3(x^2 + 1)}{x^2+1} = 3$$ к) $$\frac{7x-2}{x+2} - \frac{3x-10}{x+2} = \frac{7x - 2 - 3x + 10}{x+2} = \frac{4x + 8}{x+2} = \frac{4(x + 2)}{x+2} = 4$$ л) $$\frac{15}{c^2-5c} - \frac{3c}{c^2-5c} = \frac{15 - 3c}{c^2-5c} = \frac{3(5 - c)}{c(c-5)} = -\frac{3}{c}$$ м) $$\frac{22m+k}{15m + 5k} + \frac{8m+9k}{5k + 15m} = \frac{22m+k + 8m+9k}{15m + 5k} = \frac{30m+10k}{15m + 5k} = \frac{10(3m+k)}{5(3m + k)} = 2$$ н) $$\frac{17x-4\alpha}{x-\alpha} + \frac{6x+7\alpha}{\alpha-x} = \frac{17x-4\alpha}{x-\alpha} - \frac{6x+7\alpha}{x-\alpha} = \frac{17x-4\alpha -6x-7\alpha}{x-\alpha} = \frac{11x-11\alpha}{x-\alpha} = \frac{11(x-\alpha)}{x-\alpha} = 11$$ о) $$\frac{2m}{m-n} + \frac{2n}{n-m} = \frac{2m}{m-n} - \frac{2n}{m-n} = \frac{2m - 2n}{m-n} = \frac{2(m - n)}{m-n} = 2$$ п) $$\frac{2a+b}{a-b} + \frac{2b-5a}{a-b} = \frac{2a+b + 2b - 5a}{a-b} = \frac{-3a+3b}{a-b} = \frac{-3(a-b)}{a-b} = -3$$

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