[latex]( \frac{2}{ x^{2} -4}+ \frac{1}{2x- x^{2} } ): \frac{1}{ x^{2}+4x+4}[/latex]

[latex] ( \frac{2}{ x^{2} -4}+ \frac{1}{2x- x^{2} } ): \frac{1}{ x^{2}+4x+4} = \frac{x+2}{x} \\ \\ \\ 1)~ \frac{2}{ x^{2} -4}+ \frac{1}{2x- x^{2} } = \frac{2}{ (x-2)(x+2)}+ \frac{1}{-x(x-2)} } = \\ =\frac{2*(-x)}{ -x(x-2)(x+2)}+ \frac{x+2}{-x(x-2)(x+2)} } = \frac{-2x+x+2}{-x(x-2)(x+2)} } = \frac{-x+2}{-x(x-2)(x+2)} } = \\ = \frac{-(x-2)}{-x(x-2)(x+2)} } = \frac{-1}{-x(x+2)} = \frac{1}{x(x+2)} \\ [/latex] [latex]2)~\frac{1}{x(x+2)}: \frac{1}{ x^{2}+4x+4}=\frac{1}{x(x+2)}* \frac{x^{2}+4x+4}{ 1}= \frac{1}{x(x+2)}* \frac{(x+2)(x+2)}{ 1}= \\ =\frac{1}{x}* \frac{x+2}{ 1}= \frac{x+2}{x}[/latex]