\frac{(-\frac{1}{1-x^2}+\frac{1+x}{1-x})(\frac{2{(1-x)}^2}{x^2+4x+4}+\frac{{(x-1)}^3}{{(x+2)}^2})}{(\frac{x}{4-x^2})}
You asked:
MathBot Answer:
Evaluated
\(\displaystyle \frac{\left(-\left( \frac{1}{1 - {x}^{2}} \right) + \frac{1 + x}{1 - x}\right) \cdot \left(\frac{2 {\left( 1 - x \right)}^{2}}{{x}^{2} + 4 x + 4} + \frac{{\left( x - 1 \right)}^{3}}{{\left( x + 2 \right)}^{2}}\right)}{\frac{x}{4 - {x}^{2}}} = \frac{\left(4 - x^{2}\right) \left(\frac{2 \left(1 - x\right)^{2}}{x^{2} + 4 x + 4} + \frac{\left(x - 1\right)^{3}}{\left(x + 2\right)^{2}}\right) \left(- \frac{1}{1 - x^{2}} + \frac{x + 1}{1 - x}\right)}{x} \)
Expanded
\[\frac{\left(-\left( \frac{1}{1 - {x}^{2}} \right) + \frac{1 + x}{1 - x}\right) \cdot \left(\frac{2 {\left( 1 - x \right)}^{2}}{{x}^{2} + 4 x + 4} + \frac{{\left( x - 1 \right)}^{3}}{{\left( x + 2 \right)}^{2}}\right)}{\frac{x}{4 - {x}^{2}}} = - \frac{x^{5}}{- x^{3} - 3 x^{2} + 4} + \frac{x^{4}}{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x + 4} - \frac{x^{3}}{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x + 4} + \frac{6 x^{3}}{- x^{3} - 3 x^{2} + 4} - \frac{5 x^{2}}{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x + 4} + \frac{5 x}{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x + 4} - \frac{9 x}{- x^{3} - 3 x^{2} + 4} - \frac{4}{- x^{5} - 4 x^{4} - 3 x^{3} + 4 x^{2} + 4 x} + \frac{4}{- x^{4} - 4 x^{3} - 3 x^{2} + 4 x + 4} + \frac{4}{- x^{4} - 3 x^{3} + 4 x}\]
Factored
\[\frac{\left(-\left( \frac{1}{1 - {x}^{2}} \right) + \frac{1 + x}{1 - x}\right) \cdot \left(\frac{2 {\left( 1 - x \right)}^{2}}{{x}^{2} + 4 x + 4} + \frac{{\left( x - 1 \right)}^{3}}{{\left( x + 2 \right)}^{2}}\right)}{\frac{x}{4 - {x}^{2}}} = \left(x - 2\right) \left(x - 1\right)\]