How do you simplify the expression (1/(t-1)+1/(t+1))/(1/t-1/t^2)?

May 3, 2018

$\frac{2 {t}^{3}}{{\left(t - 1\right)}^{2} \left(t + 1\right)}$.

Explanation:

We have, $\text{The Nr.} = \frac{1}{t - 1} + \frac{1}{t + 1}$,

$= \frac{\left(t + 1\right) + \left(t - 1\right)}{\left(t - 1\right) \left(t + 1\right)}$,

$\therefore \text{ The Nr.} = \frac{2 t}{\left(t - 1\right) \left(t + 1\right)}$.

$\text{The Dr.} = \frac{1}{t} - \frac{1}{t} ^ 2$,

$= \frac{t - 1}{t} ^ 2$.

$\therefore \text{ The Exp.} = \frac{2 t}{\left(t - 1\right) \left(t + 1\right)} \div \frac{t - 1}{t} ^ 2$,

$= \frac{2 t}{\left(t - 1\right) \left(t + 1\right)} \times {t}^{2} / \left(t - 1\right)$,

$= \frac{2 {t}^{3}}{{\left(t - 1\right)}^{2} \left(t + 1\right)}$.