1. Сократите дробь: a). 15xy^4 / 10x^3y^2; б). ав-в / в^2; в). 4x^2-y^2 / 2x-y.

1. Сократите дробь: a) $\frac{15xy^4}{10x^3y^2} = \frac{3y^2}{2x^2}$ b) $\frac{ab-b}{b^2} = \frac{b(a-1)}{b^2} = \frac{a-1}{b}$ c) $\frac{4x^2-y^2}{2x-y} = \frac{(2x-y)(2x+y)}{2x-y} = 2x+y$ 2. Выполните действия: a) $\frac{3}{a} + \frac{a-3}{a+5} = \frac{3(a+5) + a(a-3)}{a(a+5)} = \frac{3a+15+a^2-3a}{a^2+5a} = \frac{a^2+15}{a^2+5a}$ b) $\frac{2x^2}{x^2-4} - \frac{2x}{x+2} = \frac{2x^2}{(x-2)(x+2)} - \frac{2x(x-2)}{(x-2)(x+2)} = \frac{2x^2 - 2x^2 + 4x}{x^2-4} = \frac{4x}{x^2-4}$ c) $\frac{7a}{a-b} - 7 = \frac{7a - 7(a-b)}{a-b} = \frac{7a - 7a + 7b}{a-b} = \frac{7b}{a-b}$ 3. Упростите выражение: $\frac{15b}{3-b} + \frac{8b}{b^2-9} \cdot \frac{7b+21}{4} = \frac{-15b}{b-3} + \frac{8b}{(b-3)(b+3)} \cdot \frac{7(b+3)}{4} = \frac{-15b}{b-3} + \frac{2b \cdot 7}{b-3} = \frac{-15b + 14b}{b-3} = \frac{-b}{b-3} = \frac{b}{3-b}$ 4. Найдите числовое значение: $(\frac{x}{x-y} - \frac{xy}{x^2-y^2}) : \frac{4x^2}{x^2-2xy+y^2} = (\frac{x(x+y) - xy}{(x-y)(x+y)}) : \frac{4x^2}{(x-y)^2} = \frac{x^2+xy-xy}{(x-y)(x+y)} \cdot \frac{(x-y)^2}{4x^2} = \frac{x^2}{(x-y)(x+y)} \cdot \frac{(x-y)^2}{4x^2} = \frac{x-y}{4(x+y)}$ Подставим $x=-2, y=-1$: $\frac{-2 - (-1)}{4(-2 + (-1))} = \frac{-2+1}{4(-3)} = \frac{-1}{-12} = \frac{1}{12}$