Упрощение выражений

91.a

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

Ответ: $$\frac{x+y}{xy}$$

91.б

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

Ответ: $$\frac{2n}{n+m}$$

91.в

$$\left(a - \frac{6a-4}{a+2}\right) \cdot \frac{a+2}{a^2-2a} = \left(\frac{a(a+2)-(6a-4)}{a+2}\right) \cdot \frac{a+2}{a(a-2)} = \frac{a^2+2a-6a+4}{a+2} \cdot \frac{a+2}{a(a-2)} = \frac{a^2-4a+4}{a+2} \cdot \frac{a+2}{a(a-2)} = \frac{(a-2)^2}{a+2} \cdot \frac{a+2}{a(a-2)} = \frac{(a-2)^2(a+2)}{(a+2)a(a-2)} = \frac{a-2}{a}$$

Ответ: $$\frac{a-2}{a}$$

92.a

$$\left(\frac{b}{a} - \frac{a}{b}\right) : (a+b) = \frac{b^2-a^2}{ab} : (a+b) = \frac{(b-a)(b+a)}{ab} \cdot \frac{1}{a+b} = \frac{(b-a)(b+a)}{ab(a+b)} = \frac{b-a}{ab}$$

Ответ: $$\frac{b-a}{ab}$$