# How do you simplify  (e^8 - e^(-8))/(e^4 - e^(-4))?

Nov 6, 2016

$\frac{{e}^{8} + 1}{e} ^ 4$

#### Explanation:

Look at the numerator of the expression
${e}^{8} - {e}^{-} 8$
=${e}^{8} - \frac{1}{e} ^ 8$ now write as one fraction
=$\frac{{e}^{16} - 1}{e} ^ 8$now factorise the numerator
=$\frac{\left({e}^{8} - 1\right) \left({e}^{8} + 1\right)}{e} ^ 8$

Now rearrange the denominator of our original expression

${e}^{4} - {e}^{-} 4$
=${e}^{4} - \frac{1}{e} ^ 4$
=$\frac{{e}^{8} - 1}{e} ^ 4$

=$\frac{\left({e}^{8} - 1\right) \left({e}^{8} + 1\right)}{e} ^ 8$divided by $\frac{{e}^{8} - 1}{e} ^ 4$
=$\frac{{e}^{8} + 1}{e} ^ 4$