Algebra Examples

$1 - e^{- 2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

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 $b = 1$ .

$\frac{(e + 1) (e - 1)}{e^{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{(e + 1) (e - 1)}{e^{2}}$

Decimal Form:

$0.86466471 \dots$