Question

Упростить выражения 21-23 (только под номером 1)

Answer 1

21.1)
$(\frac{m}{m-6} - \frac{2m}{m^2-12m+36} ) * \frac{36-m^2}{m-8} + \frac{12m}{m-6} = \\ \\ = (\frac{m}{m-6} - \frac{2m}{(m-6)^2} ) * \frac{-(m^2-6^2)}{m-8} + \frac{12m}{m-6}= \\ \\ = \frac{m(m-6)-2m}{(m-6)^2} * \frac{-(m-6)(m+6)}{m-8} + \frac{12m}{m-6} = \\ \\ = \frac{m^2-6m-2m}{(m-6)^2} * \frac{-(m-6)(m+6)}{m-8} + \frac{12m}{m-6} = \\ \\ = \frac{m^2-8m}{(m-6)^2} * \frac{-(m-6)(m+6)}{m-8} + \frac{12m}{m-6} =$
$= \frac{m(m-8) * -(m-6)(m+6)}{(m-6)(m-6) * (m-8)} + \frac{12m}{m - 6} = \\ \\ = \frac{-m(m+6)}{m-6} + \frac{12m}{m-6} = \frac{-m^2-6m+12m}{m-6} = \\ \\ = \frac{-m^2+6m}{m-6} = \frac{-m(m-6)}{m-6} = -m$

22. 1)
$( \frac{1}{x+y} - \frac{x}{y^2+xy} ) * ( \frac{y^2}{y^3-xy^2} - \frac{y}{x^2-xy} )= \\ \\ =( \frac{1}{x+y} - \frac{x}{y(y+x)} ) * ( \frac{y^2}{y^2(y-x)} - \frac{y}{-x(y-x)} )= \\ \\ = \frac{1*y -x}{y(x+y)} * ( \frac{1}{y-x} - ( - \frac{y}{x(y-x)} )) = \frac{y-x}{y(x+y)} * ( \frac{1}{y-x} +\frac{y}{x(y-x)} ) = \\ \\ = \frac{y-x}{y(x+y)} * \frac{1*x+y}{x(y-x)} = \frac{y-x}{y(x+y)} * \frac{x+y}{x(y-x)}= \frac{(y-x)*(x+y)}{y(x+y)*x(y-x)} = \frac{1}{xy}$

23.  1)
$( \frac{3}{(2-x)^2} + \frac{2}{x^2-4} ) *(x-2)^2- \frac{5x}{x+2} = \\ \\ =( \frac{3}{-(x-2)* - (x-2)} + \frac{2}{(x^2-2^2)} ) *(x-2)^2- \frac{5x}{x+2} = \\ \\ = ( \frac{3}{(x-2)^2} + \frac{2}{(x-2)(x+2)} ) *(x-2)^2- \frac{5x}{x+2} = \\ \\ = \frac{3(x+2) +2(x-2)}{(x-2)^2(x+2)} *(x-2)^2- \frac{5x}{x+2} =$
$= \frac{3x+6+2x-4}{(x-2)^2(x+2)}* \frac{(x-2)^2}{1} - \frac{5x}{x+2} = \\ \\ = \frac{(5x+2)(x-2)^2}{(x-2)^2(x+2)} - \frac{5x}{x+2} = \frac{5x+2}{x+2}- \frac{5x}{x+2} = \\ \\ = \frac{5x+2-5x}{x+2} = \frac{2}{x+2}$