Evaluate e-1/e

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

Step 1

To write $e$ as a fraction with a common denominator, multiply by $\frac{e}{e}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

Multiply $e e$ .

Raise $e$ to the power of $1$ .

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

Raise $e$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Rewrite $e^{2} - 1$ in a factored form.

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = e$ and $b = 1$ .

$\frac{(e + 1) (e - 1)}{e}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{(e + 1) (e - 1)}{e}$

Decimal Form:

$2.35040238 \dots$