Pre-Algebra Examples

$\frac{\frac{1}{x} + 6}{\frac{1}{x} - 4}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{1}{x} + 6}{\frac{1}{x} - 4}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{\frac{1}{x} + 6}{\frac{1}{x} - 4}$

Step 1.2

Combine.

$\frac{x (\frac{1}{x} + 6)}{x (\frac{1}{x} - 4)}$

Step 2

Apply the distributive property.

$\frac{x \frac{1}{x} + x \cdot 6}{x \frac{1}{x} + x \cdot - 4}$

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.

$\frac{x \frac{1}{x} + x \cdot 6}{x \frac{1}{x} + x \cdot - 4}$

Step 3.1.2

Rewrite the expression.

$\frac{1 + x \cdot 6}{x \frac{1}{x} + x \cdot - 4}$

Step 3.2

Cancel the common factor of $x$ .

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Step 3.2.1

Cancel the common factor.

$\frac{1 + x \cdot 6}{x \frac{1}{x} + x \cdot - 4}$

Step 3.2.2

Rewrite the expression.

$\frac{1 + x \cdot 6}{1 + x \cdot - 4}$

Step 4

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

$\frac{1 + 6 x}{1 + x \cdot - 4}$

Step 5

Move $- 4$ to the left of $x$ .

$\frac{1 + 6 x}{1 - 4 x}$