Выполни действия: 1) a) (2a/b^2 - 1/2a) : (1/b + 1/2a)

1. Выполняю действия: а) $\left(\frac{2a}{b^2} - \frac{1}{2a}\right) : \left(\frac{1}{b} + \frac{1}{2a}\right) = \frac{4a^2 - b^2}{2ab^2} : \frac{2a + b}{2ab} = \frac{(2a - b)(2a + b)}{2ab^2} \cdot \frac{2ab}{2a + b} = \frac{2a - b}{b}$. б) $\left(\frac{2m}{2m - 1} + 1\right) \cdot \frac{6m - 3}{4m^2 - m} = \frac{2m + 2m - 1}{2m - 1} \cdot \frac{3(2m - 1)}{m(4m - 1)} = \frac{4m - 1}{2m - 1} \cdot \frac{3(2m - 1)}{m(4m - 1)} = \frac{3}{m}$. в) $\frac{y - 3}{y + 3} \cdot \left(y + \frac{y^2}{3 - y}\right) = \frac{y - 3}{y + 3} \cdot \frac{y(3 - y) + y^2}{3 - y} = \frac{y - 3}{y + 3} \cdot \frac{3y - y^2 + y^2}{3 - y} = \frac{y - 3}{y + 3} \cdot \frac{3y}{3 - y} = -\frac{3y}{y + 3}$. г) $\left(x - \frac{5x}{x + 2}\right) : \frac{x - 3}{x + 2} = \frac{x(x + 2) - 5x}{x + 2} : \frac{x - 3}{x + 2} = \frac{x^2 + 2x - 5x}{x + 2} \cdot \frac{x + 2}{x - 3} = \frac{x^2 - 3x}{x + 2} \cdot \frac{x + 2}{x - 3} = \frac{x(x - 3)}{x + 2} \cdot \frac{x + 2}{x - 3} = x$. 2. Выполняю действия: а) $\frac{a^2 - x^2}{b^2 - 16} \cdot \frac{b + 4}{a - x} + \frac{x}{4 - b} = \frac{(a - x)(a + x)}{(b - 4)(b + 4)} \cdot \frac{b + 4}{a - x} - \frac{x}{b - 4} = \frac{a + x}{b - 4} - \frac{x}{b - 4} = \frac{a + x - x}{b - 4} = \frac{a}{b - 4}$. б) $\frac{x - y}{2x + y} + \frac{1}{x - y} \cdot \frac{x^2 - y^2}{2x + y} = \frac{x - y}{2x + y} + \frac{(x - y)(x + y)}{(x - y)(2x + y)} = \frac{x - y}{2x + y} + \frac{x + y}{2x + y} = \frac{x - y + x + y}{2x + y} = \frac{2x}{2x + y}$. в) $\left(\frac{2a^2 - a}{a^2 - a + 1} - 2\right) : \left(\frac{1}{a + 1} - \frac{a - 1}{a^2 - a + 1}\right) = \frac{2a^2 - a - 2(a^2 - a + 1)}{a^2 - a + 1} : \frac{a^2 - a + 1 - (a - 1)(a + 1)}{(a + 1)(a^2 - a + 1)} = \frac{2a^2 - a - 2a^2 + 2a - 2}{a^2 - a + 1} : \frac{a^2 - a + 1 - (a^2 - 1)}{(a + 1)(a^2 - a + 1)} = \frac{a - 2}{a^2 - a + 1} : \frac{a^2 - a + 1 - a^2 + 1}{(a + 1)(a^2 - a + 1)} = \frac{a - 2}{a^2 - a + 1} : \frac{2 - a}{(a + 1)(a^2 - a + 1)} = \frac{a - 2}{a^2 - a + 1} \cdot \frac{(a + 1)(a^2 - a + 1)}{2 - a} = -(a + 1)$. д) $\frac{6x + y}{3x} - \frac{5y^2}{x^2} \cdot \frac{x}{15y} = \frac{6x + y}{3x} - \frac{5xy^2}{15x^2y} = \frac{6x + y}{3x} - \frac{y}{3x} = \frac{6x + y - y}{3x} = \frac{6x}{3x} = 2$.