# How do you add (a-1)/(a+1 )+ (a+1)/(a-1)?

##### 1 Answer
Oct 2, 2015

Convert the denominators to a common value and simplify to get
$\textcolor{w h i t e}{\text{XXX}} \frac{2 \left({a}^{2} + 1\right)}{{a}^{2} - 1}$

#### Explanation:

$\textcolor{red}{\frac{a - 1}{a + 1}} + \textcolor{b l u e}{\frac{a + 1}{a - 1}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{\frac{a - 1}{a + 1}} \cdot \frac{a - 1}{a - 1} + \left(\frac{\textcolor{b l u e}{a + 1}}{a - 1}\right) \cdot \frac{a + 1}{a + 1}$

color(white)("XXX")=(color(green)((a-1)^2)+color(brown)((a+1)^2))/((a-1)(a+1)

$\textcolor{w h i t e}{\text{XXX}} = \frac{\textcolor{g r e e n}{{a}^{2} - 2 a + 1} + \textcolor{b r o w n}{{a}^{2} + 2 a + 1}}{\left(a - 1\right) \left(a + 1\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{2 \left({a}^{2} + 1\right)}{{a}^{2} - 1}$