Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Let $u = 2^{x}$ . Substitute $u$ for all occurrences of $2^{x}$ .

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

Step 1.3

Factor $u$ out of $u^{2} - u$ .

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Step 1.3.1

Factor $u$ out of $u^{2}$ .

$\frac{u \cdot u - u}{2^{x} - 1}$

Step 1.3.2

Factor $u$ out of $- u$ .

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

Step 1.3.3

Factor $u$ out of $u \cdot u + u \cdot - 1$ .

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

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

Step 1.4

Replace all occurrences of $u$ with $2^{x}$ .

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

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

Step 2

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

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Step 2.1

Cancel the common factor.

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

Step 2.2

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

$2^{x}$

$2^{x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$