Algebra Examples

$\frac{4 + \frac{2}{x}}{\frac{x}{3} + \frac{1}{6}}$

Step 1

Multiply the numerator and denominator of the fraction by $x \cdot 6$ .

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Step 1.1

Multiply $\frac{4 + \frac{2}{x}}{\frac{x}{3} + \frac{1}{6}}$ by $\frac{x \cdot 6}{x \cdot 6}$ .

$\frac{x \cdot 6}{x \cdot 6} \cdot \frac{4 + \frac{2}{x}}{\frac{x}{3} + \frac{1}{6}}$

Step 1.2

Combine.

$\frac{x \cdot 6 (4 + \frac{2}{x})}{x \cdot 6 (\frac{x}{3} + \frac{1}{6})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 6 \cdot 4 + x \cdot 6 \frac{2}{x}}{x \cdot 6 \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

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 $x \cdot 6$ .

$\frac{x \cdot 6 \cdot 4 + x (6) \frac{2}{x}}{x \cdot 6 \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.1.2

Cancel the common factor.

$\frac{x \cdot 6 \cdot 4 + x \cdot 6 \frac{2}{x}}{x \cdot 6 \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.1.3

Rewrite the expression.

$\frac{x \cdot 6 \cdot 4 + 6 \cdot 2}{x \cdot 6 \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.2

Multiply $6$ by $2$ .

$\frac{x \cdot 6 \cdot 4 + 12}{x \cdot 6 \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $x \cdot 6$ .

$\frac{x \cdot 6 \cdot 4 + 12}{3 (x \cdot 2) \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.3.2

Cancel the common factor.

$\frac{x \cdot 6 \cdot 4 + 12}{3 (x \cdot 2) \frac{x}{3} + x \cdot 6 \frac{1}{6}}$

Step 3.3.3

Rewrite the expression.

$\frac{x \cdot 6 \cdot 4 + 12}{x \cdot 2 x + x \cdot 6 \frac{1}{6}}$

Step 3.4

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

$\frac{x \cdot 6 \cdot 4 + 12}{2 (x^{1} x) + x \cdot 6 \frac{1}{6}}$

Step 3.5

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

$\frac{x \cdot 6 \cdot 4 + 12}{2 (x^{1} x^{1}) + x \cdot 6 \frac{1}{6}}$

Step 3.6

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

$\frac{x \cdot 6 \cdot 4 + 12}{2 x^{1 + 1} + x \cdot 6 \frac{1}{6}}$

Step 3.7

Add $1$ and $1$ .

$\frac{x \cdot 6 \cdot 4 + 12}{2 x^{2} + x \cdot 6 \frac{1}{6}}$

Step 3.8

Cancel the common factor of $6$ .

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Step 3.8.1

Factor $6$ out of $x \cdot 6$ .

$\frac{x \cdot 6 \cdot 4 + 12}{2 x^{2} + 6 \cdot x \frac{1}{6}}$

Step 3.8.2

Cancel the common factor.

$\frac{x \cdot 6 \cdot 4 + 12}{2 x^{2} + 6 \cdot x \frac{1}{6}}$

Step 3.8.3

Rewrite the expression.

$\frac{x \cdot 6 \cdot 4 + 12}{2 x^{2} + x}$

Step 4

Simplify the numerator.

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Step 4.1

Move $6$ to the left of $x$ .

$\frac{6 \cdot x \cdot 4 + 12}{2 x^{2} + x}$

Step 4.2

Multiply $4$ by $6$ .

$\frac{24 x + 12}{2 x^{2} + x}$

Step 4.3

Factor $12$ out of $24 x + 12$ .

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Step 4.3.1

Factor $12$ out of $24 x$ .

$\frac{12 (2 x) + 12}{2 x^{2} + x}$

Step 4.3.2

Factor $12$ out of $12$ .

$\frac{12 (2 x) + 12 (1)}{2 x^{2} + x}$

Step 4.3.3

Factor $12$ out of $12 (2 x) + 12 (1)$ .

$\frac{12 (2 x + 1)}{2 x^{2} + x}$

Step 5

Simplify terms.

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Step 5.1

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

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Step 5.1.1

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

$\frac{12 (2 x + 1)}{x (2 x) + x}$

Step 5.1.2

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

$\frac{12 (2 x + 1)}{x (2 x) + x^{1}}$

Step 5.1.3

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

$\frac{12 (2 x + 1)}{x (2 x) + x \cdot 1}$

Step 5.1.4

Factor $x$ out of $x (2 x) + x \cdot 1$ .

$\frac{12 (2 x + 1)}{x (2 x + 1)}$

Step 5.2

Cancel the common factor of $2 x + 1$ .

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Step 5.2.1

Cancel the common factor.

$\frac{12 (2 x + 1)}{x (2 x + 1)}$

Step 5.2.2

Rewrite the expression.

$\frac{12}{x}$