# Question #d96aa

Apr 27, 2017

$\frac{{e}^{2} - 2 e - 1}{e}$

#### Explanation:

First, let's discuss ${e}^{1} \mathmr{and} {e}^{-} 1$

${e}^{1}$ just means $e$
${e}^{-} 1$ means $\frac{1}{e}$
[If there was ${e}^{-} 2$ it would have meant $\frac{1}{e} ^ 2$]

So now it becomes really simple.

Also ${\left(- 1\right)}^{3} = - 1$
[$- 1$ raised to any odd number is $- 1$ and if it is raised to any even number, it is $1$]

Let's solve this

$\left(e - \frac{1}{3}\right) - \left(\frac{1}{e} + \frac{1}{3}\right)$
$e - \frac{1}{3} - \frac{1}{e} - \frac{1}{3}$

This becomes $\frac{3 {e}^{2} - 2 e - 3}{3 e}$