Algebra Examples

$\frac{2^{2 x} - 1}{2^{x} + 1}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $2^{2 x}$ as ${(2^{x})}^{2}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Cancel the common factor of $2^{x} + 1$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $2^{x} - 1$ by $1$ .

$2^{x} - 1$