Algebra Examples

$\frac{9 + \frac{3}{x}}{\frac{x}{4} + \frac{1}{12}}$

Step 1

Multiply the numerator and denominator of the fraction by $x \cdot 12$ .

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Step 1.1

Multiply $\frac{9 + \frac{3}{x}}{\frac{x}{4} + \frac{1}{12}}$ by $\frac{x \cdot 12}{x \cdot 12}$ .

$\frac{x \cdot 12}{x \cdot 12} \cdot \frac{9 + \frac{3}{x}}{\frac{x}{4} + \frac{1}{12}}$

Step 1.2

Combine.

$\frac{x \cdot 12 (9 + \frac{3}{x})}{x \cdot 12 (\frac{x}{4} + \frac{1}{12})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 12 \cdot 9 + x \cdot 12 \frac{3}{x}}{x \cdot 12 \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

Factor $x$ out of $x \cdot 12$ .

$\frac{x \cdot 12 \cdot 9 + x (12) \frac{3}{x}}{x \cdot 12 \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.1.2

Cancel the common factor.

$\frac{x \cdot 12 \cdot 9 + x \cdot 12 \frac{3}{x}}{x \cdot 12 \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.1.3

Rewrite the expression.

$\frac{x \cdot 12 \cdot 9 + 12 \cdot 3}{x \cdot 12 \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.2

Multiply $12$ by $3$ .

$\frac{x \cdot 12 \cdot 9 + 36}{x \cdot 12 \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $x \cdot 12$ .

$\frac{x \cdot 12 \cdot 9 + 36}{4 (x \cdot 3) \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.3.2

Cancel the common factor.

$\frac{x \cdot 12 \cdot 9 + 36}{4 (x \cdot 3) \frac{x}{4} + x \cdot 12 \frac{1}{12}}$

Step 3.3.3

Rewrite the expression.

$\frac{x \cdot 12 \cdot 9 + 36}{x \cdot 3 x + x \cdot 12 \frac{1}{12}}$

Step 3.4

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

$\frac{x \cdot 12 \cdot 9 + 36}{3 (x^{1} x) + x \cdot 12 \frac{1}{12}}$

Step 3.5

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

$\frac{x \cdot 12 \cdot 9 + 36}{3 (x^{1} x^{1}) + x \cdot 12 \frac{1}{12}}$

Step 3.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x \cdot 12 \cdot 9 + 36}{3 x^{1 + 1} + x \cdot 12 \frac{1}{12}}$

Step 3.7

Add $1$ and $1$ .

$\frac{x \cdot 12 \cdot 9 + 36}{3 x^{2} + x \cdot 12 \frac{1}{12}}$

Step 3.8

Cancel the common factor of $12$ .

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Step 3.8.1

Factor $12$ out of $x \cdot 12$ .

$\frac{x \cdot 12 \cdot 9 + 36}{3 x^{2} + 12 \cdot x \frac{1}{12}}$

Step 3.8.2

Cancel the common factor.

$\frac{x \cdot 12 \cdot 9 + 36}{3 x^{2} + 12 \cdot x \frac{1}{12}}$

Step 3.8.3

Rewrite the expression.

$\frac{x \cdot 12 \cdot 9 + 36}{3 x^{2} + x}$

Step 4

Simplify the numerator.

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Step 4.1

Move $12$ to the left of $x$ .

$\frac{12 \cdot x \cdot 9 + 36}{3 x^{2} + x}$

Step 4.2

Multiply $9$ by $12$ .

$\frac{108 x + 36}{3 x^{2} + x}$

Step 4.3

Factor $36$ out of $108 x + 36$ .

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Step 4.3.1

Factor $36$ out of $108 x$ .

$\frac{36 (3 x) + 36}{3 x^{2} + x}$

Step 4.3.2

Factor $36$ out of $36$ .

$\frac{36 (3 x) + 36 (1)}{3 x^{2} + x}$

Step 4.3.3

Factor $36$ out of $36 (3 x) + 36 (1)$ .

$\frac{36 (3 x + 1)}{3 x^{2} + x}$

Step 5

Factor $x$ out of $3 x^{2} + x$ .

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Step 5.1

Factor $x$ out of $3 x^{2}$ .

$\frac{36 (3 x + 1)}{x (3 x) + x}$

Step 5.2

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

$\frac{36 (3 x + 1)}{x (3 x) + x^{1}}$

Step 5.3

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

$\frac{36 (3 x + 1)}{x (3 x) + x \cdot 1}$

Step 5.4

Factor $x$ out of $x (3 x) + x \cdot 1$ .

$\frac{36 (3 x + 1)}{x (3 x + 1)}$

Step 6

Cancel the common factor of $3 x + 1$ .

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Step 6.1

Cancel the common factor.

$\frac{36 (3 x + 1)}{x (3 x + 1)}$

Step 6.2

Rewrite the expression.

$\frac{36}{x}$