10.2. Выполните действия

### 10.2 1) $\frac{b+4}{(b-3)^2} : \frac{(b-4)(b+4)}{2(b-3)} - \frac{2}{b-4} = \frac{b+4}{(b-3)^2} \cdot \frac{2(b-3)}{(b-4)(b+4)} - \frac{2}{b-4} = \frac{2}{(b-3)(b-4)} - \frac{2(b-3)}{(b-3)(b-4)} = \frac{2 - 2b + 6}{(b-3)(b-4)} = \frac{8 - 2b}{(b-3)(b-4)} = \frac{-2(b-4)}{(b-3)(b-4)} = -\frac{2}{b-3} = \frac{2}{3-b}$ 2) $\frac{2x}{(x-y)(x+y)} : \left(\frac{1}{(x+y)^2} - \frac{1}{(y-x)(y+x)}\right) = \frac{2x}{(x-y)(x+y)} : \left(\frac{1}{(x+y)^2} + \frac{1}{(x-y)(x+y)}\right) = \frac{2x}{(x-y)(x+y)} : \frac{x-y + x+y}{(x+y)^2(x-y)} = \frac{2x}{(x-y)(x+y)} \cdot \frac{(x+y)^2(x-y)}{2x} = x+y$ 3) $\left(\frac{2a-3}{(a-2)^2} - \frac{a-1}{a(a-2)}\right) : \frac{a^2-2}{a(a^2-4)} = \frac{a(2a-3) - (a-1)(a-2)}{a(a-2)^2} : \frac{a^2-2}{a(a-2)(a+2)} = \frac{2a^2-3a - (a^2-3a+2)}{a(a-2)^2} \cdot \frac{a(a-2)(a+2)}{a^2-2} = \frac{a^2-2}{a(a-2)^2} \cdot \frac{a(a-2)(a+2)}{a^2-2} = \frac{a+2}{a-2}$ ### 10.3 1) $\left(\frac{15 - x(x-7) - 7(x-7)}{x-7}\right) \cdot \frac{7-x}{(x-8)^2} = \frac{15 - x^2 + 7x - 7x + 49}{x-7} \cdot \frac{-(x-7)}{(x-8)^2} = \frac{64 - x^2}{x-7} \cdot \frac{-(x-7)}{(x-8)^2} = \frac{-(8-x)(8+x)}{1} \cdot \frac{1}{(8-x)^2} = \frac{8+x}{8-x}$ 2) $\left(\frac{b^2 + 2ab + a^2}{ab^2}\right) \cdot \frac{ab}{(a-b)(a+b)} - \frac{2}{a-b} = \frac{(a+b)^2}{ab^2} \cdot \frac{ab}{(a-b)(a+b)} - \frac{2}{a-b} = \frac{a+b}{b(a-b)} - \frac{2}{a-b} = \frac{a+b - 2b}{b(a-b)} = \frac{a-b}{b(a-b)} = \frac{1}{b}$