Упростите рациональное выражение:
а) $\frac{x + y}{x} - \frac{x}{x - y} + \frac{y^2}{x^2 - xy}$;
б) $\frac{1}{m + 2} + \frac{1}{m - 2} - \frac{4}{m^2 - 4}$;
в) $\frac{3x^2 + 3xy}{4xy + 6ay} * (\frac{x}{ax + ay} + \frac{3}{2x + 2y})$;
г) $(\frac{c - d}{c^2 + cd} - \frac{c}{d^2 + cd}) : (\frac{d^2}{c^3 - cd^2} + \frac{1}{c + d})$.
$\frac{x + y}{x} - \frac{x}{x - y} + \frac{y^2}{x^2 - xy} = \frac{x + y}{x} - \frac{x}{x - y} + \frac{y^2}{x(x - y)} = \frac{(x + y)(x - y) - x * x + y^2}{x(x - y)} = \frac{x^2 - y^2 - x^2 + y^2}{x(x - y)} = \frac{0}{x - y} = 0$
$\frac{1}{m + 2} + \frac{1}{m - 2} - \frac{4}{m^2 - 4} = \frac{1}{m + 2} + \frac{1}{m - 2} - \frac{4}{(m - 2)(m + 2)} = \frac{m - 2 + m + 2 - 4}{(m - 2)(m + 2)} = \frac{2m - 4}{(m - 2)(m + 2)} = \frac{2(m - 2)}{(m - 2)(m + 2)} = \frac{2}{m + 2}$
$\frac{3x^2 + 3xy}{4xy + 6ay} * (\frac{x}{ax + ay} + \frac{3}{2x + 2y}) = \frac{3x(x + y)}{2y(2x + 3a)} * (\frac{x}{a(x + y) + \frac{3}{2(x + y)}}) = \frac{3x(x + y)}{2y(2x + 3a)} * \frac{2x + 3a}{2a(x + y)} = \frac{3x}{2y * 2a} = \frac{3x}{4ay}$
$(\frac{c - d}{c^2 + cd} - \frac{c}{d^2 + cd}) : (\frac{d^2}{c^3 - cd^2} + \frac{1}{c + d}) = (\frac{c - d}{c(c + d)} - \frac{c}{d(d + c)}) : (\frac{d^2}{c(c^2 - d^2)} + \frac{1}{c + d}) = \frac{d(c - d) - c * c}{cd(c + d)} : (\frac{d^2}{c(c - d)(c + d) + \frac{1}{c + d}}) = \frac{cd - d^2 - c^2}{cd(c + d)} : \frac{d^2 + c(c - d)}{c(c - d)(c + d)} = \frac{cd - d^2 - c^2}{cd(c + d)} * \frac{c(c - d)(c + d)}{d^2 + c^2 - cd} = \frac{-(d^2 + c^2 - cd)(c - d)}{d(d^2 + c^2 - cd)} = \frac{d - c}{d}$
Пожауйста, оцените решение
