Выполните действия. Номер 41.1 2) 4) 6) пример. Тема Тождественные преобразования...

Решите задачу:

$2) ( \frac{n}{m^2} + \frac{n^2}{m^3} ): ( \frac{m^2}{3n^2} + \frac{m}{3n} )= \frac{nm+n^2}{m^3} : \frac{m^2+mn}{3n^2}= \\ \\ = \frac{n(m+n)}{m^3} : \frac{m(m+n)}{3n^2} = \frac{n(m+n)}{m^3} * \frac{3n^2}{m(m+n)} = \\ \\ = \frac{n(m+n)*3n^2}{m^3*m(m+n)} = \frac{n*1*3n^2}{m^3*m*1} = \frac{3n^3}{m^4}$

$4) \frac{x-y}{x} - \frac{5y}{x^2} * \frac{x^2-xy}{5y} = \frac{x-y}{x} - \frac{5y}{x^2} * \frac{x(x-y)}{5y} = \\ \\ = \frac{x-y}{x} - \frac{5y*x(x-y)}{x^2*5y} = \frac{x-y}{x} - \frac{1*1*(x-y)}{x*1} = \\ \\ = \frac{x-y}{x} - \frac{x-y}{x} = \frac{x-y-(x-y)}{x} = \frac{x-y-x+y}{x} =0$

$6) ( \frac{4a}{a-2} - a) : \frac{a+2}{a-2} = \frac{4a-a(a-2)}{a-2} * \frac{a-2}{a+2} = \\ \\ = \frac{4a-a^2+2a}{a-2} * \frac{a-2}{a+2} = \frac{-a^2+6a}{a-2} * \frac{a-2}{a+2} = \\ \\ = \frac{-a(a-6)}{a-2} * \frac{a-2}{a+2} = \frac{-a(a-6)(a-2)}{(a-2)(a+2)} = \frac{-a(a-6)}{a+2} = \\ \\ = - \frac{a(a-6)}{a+2}$