Algebra Examples

$\frac{4^{x} + 2^{x}}{2^{x}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4^{x}$ as ${(2^{2})}^{x}$ .

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

Step 1.2

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

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

Step 1.3

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

$\frac{u^{2} + u}{2^{x}}$

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.4.3

Factor $u$ out of $u^{1}$ .

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

Step 1.4.4

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

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

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

Step 1.5

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

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

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

Step 2

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

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Step 2.1

Cancel the common factor.

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

Step 2.2

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

$2^{x} + 1$

$2^{x} + 1$

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