Выполните действия для алгебраических выражений

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