Precalculus Examples

$\frac{5 + \frac{1}{x}}{3 - \frac{1}{x}}$

Step 1

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

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Step 1.1

Multiply $\frac{5 + \frac{1}{x}}{3 - \frac{1}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{5 + \frac{1}{x}}{3 - \frac{1}{x}}$

Step 1.2

Combine.

$\frac{x (5 + \frac{1}{x})}{x (3 - \frac{1}{x})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 5 + x \frac{1}{x}}{x \cdot 3 + x (- \frac{1}{x})}$

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.

$\frac{x \cdot 5 + x \frac{1}{x}}{x \cdot 3 + x (- \frac{1}{x})}$

Step 3.1.2

Rewrite the expression.

$\frac{x \cdot 5 + 1}{x \cdot 3 + x (- \frac{1}{x})}$

Step 3.2

Cancel the common factor of $x$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{x}$ into the numerator.

$\frac{x \cdot 5 + 1}{x \cdot 3 + x \frac{- 1}{x}}$

Step 3.2.2

Cancel the common factor.

$\frac{x \cdot 5 + 1}{x \cdot 3 + x \frac{- 1}{x}}$

Step 3.2.3

Rewrite the expression.

$\frac{x \cdot 5 + 1}{x \cdot 3 - 1}$

Step 4

Move $5$ to the left of $x$ .

$\frac{5 x + 1}{x \cdot 3 - 1}$

Step 5

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

$\frac{5 x + 1}{3 x - 1}$