Question

Упростите выражения. Пожалуйста, очень нужно.

Answer 1

а)
$(\frac{2}{x^2-4}+\frac{1}{2x-x^2}):\frac{1}{x^2+4x+4}= \\\\ =(\frac{2}{(x-2)(x+2)}+\frac{1}{x(2-x)})\cdot (x^2+4x+4)= \\\\ =(\frac{2}{(x-2)(x+2)}-\frac{1}{x(x-2)})\cdot (x^2+2\cdot2x+4)= \\\\ =(\frac{2x}{x(x-2)(x+2)}-\frac{x+2}{x(x-2)(x+2)})\cdot (x+2)^2= \\\\ =\frac{2x-x-2}{x(x-2)(x+2)}\cdot (x+2)^2= \\\\ =\frac{(x-2)(x+2)(x+2)}{x(x-2)(x+2)}= \\\\ =\frac{x+2}{x}$


б)
$(\frac{6}{y^2-9}+\frac{1}{3-y})\cdot\frac{y^2+6y+9}{5}= \\\\ =(\frac{6}{(y-3)(y+3)}-\frac{1}{y-3})\cdot\frac{y^2+2\cdot2y+3^2}{5}= \\\\ =(\frac{6}{(y-3)(y+3)}-\frac{y+3}{(y-3)(y+3)})\cdot\frac{(y+3)^2}{5}= \\\\ =\frac{6-y-3}{(y-3)(y+3)}\cdot\frac{(y+3)^2}{5}= \\\\ =\frac{3-y}{y-3}\cdot\frac{y+3}{5}= \\\\ =-\frac{y+3}{5}$