Algebra Examples

$\frac{\frac{x^{2}}{9} + \frac{1}{4}}{6 x}$

Step 1

Simplify the numerator.

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Step 1.1

To write $\frac{x^{2}}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{x^{2}}{9} \cdot \frac{4}{4} + \frac{1}{4}}{6 x}$

Step 1.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{x^{2}}{9} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{9}{9}}{6 x}$

Step 1.3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x^{2}}{9}$ by $\frac{4}{4}$ .

$\frac{\frac{x^{2} \cdot 4}{9 \cdot 4} + \frac{1}{4} \cdot \frac{9}{9}}{6 x}$

Step 1.3.2

Multiply $9$ by $4$ .

$\frac{\frac{x^{2} \cdot 4}{36} + \frac{1}{4} \cdot \frac{9}{9}}{6 x}$

Step 1.3.3

Multiply $\frac{1}{4}$ by $\frac{9}{9}$ .

$\frac{\frac{x^{2} \cdot 4}{36} + \frac{9}{4 \cdot 9}}{6 x}$

Step 1.3.4

Multiply $4$ by $9$ .

$\frac{\frac{x^{2} \cdot 4}{36} + \frac{9}{36}}{6 x}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{x^{2} \cdot 4 + 9}{36}}{6 x}$

Step 1.5

Move $4$ to the left of $x^{2}$ .

$\frac{\frac{4 x^{2} + 9}{36}}{6 x}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 x^{2} + 9}{36} \cdot \frac{1}{6 x}$

Step 3

Multiply $\frac{4 x^{2} + 9}{36} \cdot \frac{1}{6 x}$ .

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Step 3.1

Multiply $\frac{4 x^{2} + 9}{36}$ by $\frac{1}{6 x}$ .

$\frac{4 x^{2} + 9}{36 (6 x)}$

Step 3.2

Multiply $6$ by $36$ .

$\frac{4 x^{2} + 9}{216 x}$