# (x/(x-2))^2 + (x/(x+2))^2=?

##### 2 Answers
Apr 4, 2018

${x}^{2} / {\left(x - 2\right)}^{2} + {x}^{2} / {\left(x + 2\right)}^{2}$

$\implies {x}^{2} \left[\frac{1}{x - 2} ^ 2 + \frac{1}{x + 2} ^ 2\right]$

$\implies {x}^{2} \left[\frac{{\left(x + 2\right)}^{2} + {\left(x - 2\right)}^{2}}{{\left(x - 2\right)}^{2} {\left(x + 2\right)}^{2}}\right]$

$\implies {x}^{2} \left[\frac{{x}^{2} + 4 + 4 x + {x}^{2} + 4 - 4 x}{{\left(\left(x - 2\right) \left(x + 2\right)\right)}^{2}}\right]$

$\implies {x}^{2} \left[\frac{2 {x}^{2} + 8}{{x}^{2} - 4} ^ 2\right]$

$\implies 2 {x}^{2} \left[\frac{{x}^{2} + 4}{{x}^{2} - 4} ^ 2\right]$

Apr 4, 2018

We start by expanding:

${x}^{2} / \left({x}^{2} - 4 x + 4\right) + {x}^{2} / \left({x}^{2} + 4 x + 4\right)$

$\frac{{x}^{2} \left({x}^{2} + 4 x + 4\right) + {x}^{2} \left({x}^{2} - 4 x + 4\right)}{{\left(x + 2\right)}^{2} {\left(x - 2\right)}^{2}}$

$\frac{{x}^{4} + 4 {x}^{3} + 4 {x}^{2} + {x}^{4} - 4 {x}^{3} + 4 {x}^{2}}{{\left(x + 2\right)}^{2} {\left(x - 2\right)}^{2}}$

(2x^4 + 8x^2)/((x +2)^2(x - 2)^2

$\frac{2 {x}^{2} \left({x}^{2} + 4\right)}{{\left(x + 2\right)}^{2} {\left(x - 2\right)}^{2}}$

Hopefully this helps!