Pre-Algebra Examples

$\frac{\frac{6}{w} + \frac{7}{x}}{\frac{7}{w} - \frac{6}{x}}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{6}{w} + \frac{7}{x}}{\frac{7}{w} - \frac{6}{x}}$ by $\frac{w x}{w x}$ .

$\frac{w x}{w x} \cdot \frac{\frac{6}{w} + \frac{7}{x}}{\frac{7}{w} - \frac{6}{x}}$

Step 1.2

Combine.

$\frac{w x (\frac{6}{w} + \frac{7}{x})}{w x (\frac{7}{w} - \frac{6}{x})}$

Step 2

Apply the distributive property.

$\frac{w x \frac{6}{w} + w x \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $w$ .

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Step 3.1.1

Factor $w$ out of $w x$ .

$\frac{w (x) \frac{6}{w} + w x \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.1.2

Cancel the common factor.

$\frac{w x \frac{6}{w} + w x \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.1.3

Rewrite the expression.

$\frac{x \cdot 6 + w x \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.2

Cancel the common factor of $x$ .

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Step 3.2.1

Factor $x$ out of $w x$ .

$\frac{x \cdot 6 + x w \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.2.2

Cancel the common factor.

$\frac{x \cdot 6 + x w \frac{7}{x}}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.2.3

Rewrite the expression.

$\frac{x \cdot 6 + w \cdot 7}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.3

Cancel the common factor of $w$ .

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Step 3.3.1

Factor $w$ out of $w x$ .

$\frac{x \cdot 6 + w \cdot 7}{w (x) \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.3.2

Cancel the common factor.

$\frac{x \cdot 6 + w \cdot 7}{w x \frac{7}{w} + w x (- \frac{6}{x})}$

Step 3.3.3

Rewrite the expression.

$\frac{x \cdot 6 + w \cdot 7}{x \cdot 7 + w x (- \frac{6}{x})}$

Step 3.4

Cancel the common factor of $x$ .

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Step 3.4.1

Move the leading negative in $- \frac{6}{x}$ into the numerator.

$\frac{x \cdot 6 + w \cdot 7}{x \cdot 7 + w x \frac{- 6}{x}}$

Step 3.4.2

Factor $x$ out of $w x$ .

$\frac{x \cdot 6 + w \cdot 7}{x \cdot 7 + x w \frac{- 6}{x}}$

Step 3.4.3

Cancel the common factor.

$\frac{x \cdot 6 + w \cdot 7}{x \cdot 7 + x w \frac{- 6}{x}}$

Step 3.4.4

Rewrite the expression.

$\frac{x \cdot 6 + w \cdot 7}{x \cdot 7 + w \cdot - 6}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{6 \cdot x + w \cdot 7}{x \cdot 7 + w \cdot - 6}$

Step 4.2

Move $7$ to the left of $w$ .

$\frac{6 x + 7 w}{x \cdot 7 + w \cdot - 6}$

Step 5

Simplify the denominator.

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Step 5.1

Move $7$ to the left of $x$ .

$\frac{6 x + 7 w}{7 \cdot x + w \cdot - 6}$

Step 5.2

Move $- 6$ to the left of $w$ .

$\frac{6 x + 7 w}{7 x - 6 w}$