Выполни действия: a) $(\frac{x}{y^2} - \frac{1}{x}) : (\frac{1}{y} + \frac{1}{x})$; б) $(\frac{a}{m^2} + \frac{a^2}{m^3}) : (\frac{m^2}{a^2} + \frac{m}{a})$; в) $\frac{ab + b^2}{3} : \frac{b^3}{3a} + \frac{a + b}{b}$; г) $\frac{x - y}{x} - \frac{5y}{x^2} * \frac{x^2 - xy}{5y}$

a) $\frac{x}{y^2} - \frac{1}{x} : (\frac{1}{y} + \frac{1}{x})$ $\frac{x}{y^2} - \frac{1}{x} = \frac{x^2 - y^2}{xy^2}$ $\frac{1}{y} + \frac{1}{x} = \frac{x + y}{xy}$ $(\frac{x^2 - y^2}{xy^2}) : (\frac{x + y}{xy}) = \frac{(x - y)(x + y)}{xy^2} * \frac{xy}{x + y} = \frac{x - y}{y}$ **Ответ: $\frac{x - y}{y}$** б) $(\frac{a}{m^2} + \frac{a^2}{m^3}) : (\frac{m^2}{a^2} + \frac{m}{a})$ $\frac{a}{m^2} + \frac{a^2}{m^3} = \frac{am + a^2}{m^3} = \frac{a(m + a)}{m^3}$ $\frac{m^2}{a^2} + \frac{m}{a} = \frac{m^2 + am}{a^2} = \frac{m(m + a)}{a^2}$ $\frac{a(m + a)}{m^3} : \frac{m(m + a)}{a^2} = \frac{a(m + a)}{m^3} * \frac{a^2}{m(m + a)} = \frac{a^3}{m^4}$ **Ответ: $\frac{a^3}{m^4}$** в) $\frac{ab + b^2}{3} : \frac{b^3}{3a} + \frac{a + b}{b}$ $\frac{ab + b^2}{3} : \frac{b^3}{3a} = \frac{b(a + b)}{3} * \frac{3a}{b^3} = \frac{a(a + b)}{b^2}$ $\frac{a(a + b)}{b^2} + \frac{a + b}{b} = \frac{a(a + b) + b(a + b)}{b^2} = \frac{(a + b)(a + b)}{b^2} = \frac{(a + b)^2}{b^2}$ **Ответ: $\frac{(a + b)^2}{b^2}$** г) $\frac{x - y}{x} - \frac{5y}{x^2} * \frac{x^2 - xy}{5y}$ $\frac{5y}{x^2} * \frac{x^2 - xy}{5y} = \frac{5y}{x^2} * \frac{x(x - y)}{5y} = \frac{x - y}{x}$ $\frac{x - y}{x} - \frac{x - y}{x} = 0$ **Ответ: 0**