Algebra Examples

$\frac{\frac{x}{4} + \frac{1}{8}}{\frac{x^{2}}{4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{x}{4} + \frac{1}{8}) \frac{4}{x^{2}}$

Step 2

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{x}{4} \cdot \frac{2}{2} + \frac{1}{8}) \frac{4}{x^{2}}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x}{4}$ by $\frac{2}{2}$ .

$(\frac{x \cdot 2}{4 \cdot 2} + \frac{1}{8}) \frac{4}{x^{2}}$

Step 3.2

Multiply $4$ by $2$ .

$(\frac{x \cdot 2}{8} + \frac{1}{8}) \frac{4}{x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 1}{8} \cdot \frac{4}{x^{2}}$

Step 5

Move $2$ to the left of $x$ .

$\frac{2 x + 1}{8} \cdot \frac{4}{x^{2}}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $4$ .

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Step 6.1.1

Factor $4$ out of $8$ .

$\frac{2 x + 1}{4 (2)} \cdot \frac{4}{x^{2}}$

Step 6.1.2

Cancel the common factor.

$\frac{2 x + 1}{4 \cdot 2} \cdot \frac{4}{x^{2}}$

Step 6.1.3

Rewrite the expression.

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

Step 6.2

Multiply $\frac{2 x + 1}{2}$ by $\frac{1}{x^{2}}$ .

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