Algebra Examples

$\frac{4 + \frac{2}{x}}{3 - \frac{2}{x}}$

Step 1

Multiply the numerator and denominator of the fraction by $x$ .

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Step 1.1

Multiply $\frac{4 + \frac{2}{x}}{3 - \frac{2}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{4 + \frac{2}{x}}{3 - \frac{2}{x}}$

Step 1.2

Combine.

$\frac{x (4 + \frac{2}{x})}{x (3 - \frac{2}{x})}$

Step 2

Apply the distributive property.

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

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

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $x$ .

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Step 3.2.1

Move the leading negative in $- \frac{2}{x}$ into the numerator.

$\frac{x \cdot 4 + 2}{x \cdot 3 + x \frac{- 2}{x}}$

Step 3.2.2

Cancel the common factor.

$\frac{x \cdot 4 + 2}{x \cdot 3 + x \frac{- 2}{x}}$

Step 3.2.3

Rewrite the expression.

$\frac{x \cdot 4 + 2}{x \cdot 3 - 2}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $2$ out of $x \cdot 4 + 2$ .

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Step 4.1.1

Factor $2$ out of $x \cdot 4$ .

$\frac{2 (x \cdot 2) + 2}{x \cdot 3 - 2}$

Step 4.1.2

Factor $2$ out of $2$ .

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

Step 4.1.3

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

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

Step 4.2

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

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

Step 5

Move $3$ to the left of $x$ .

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