Question

№578(4) данные выражения a^2-4/x^2-9 : a^2-2a/xy+3y + 2-y/x-3 !

Answer 1

$\frac{a^2-4}{x^2-9} : \frac{a^2-2a}{xy+3y} + \frac{2-y}{x-3}= \frac{a^2-4}{x^2-9} \cdot \frac{xy+3y}{a^2-2a} + \frac{2-y}{x-3}= \\ \\ = \frac{(a-2)(a+2)}{(x-3)(x+3)} \cdot \frac{y(x+3)}{a(a-2)} + \frac{2-y}{x-3}= \\ \\ = \frac{a+2}{x-3} \cdot \frac{y}{a} + \frac{(2-y)a}{(x-3)a}= \frac{ay+2y+2a-ya}{(x-3)a}= \frac{2(y+a)}{(x-3)a}$