Algebra Examples

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

Step 1

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

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

Step 2

Combine fractions.

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Step 2.1

Combine $- e$ and $\frac{e}{e}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply $- e e$ .

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Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Add $1$ and $1$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 2.35040238 \dots$