Algebra Examples

$\frac{(\frac{x}{4}) - 3}{9 (\frac{x}{4}) - 5}$

Step 1

Multiply the numerator and denominator of the fraction by $4$ .

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Step 1.1

Multiply $\frac{\frac{x}{4} - 3}{9 \frac{x}{4} - 5}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{\frac{x}{4} - 3}{9 \frac{x}{4} - 5}$

Step 1.2

Combine.

$\frac{4 (\frac{x}{4} - 3)}{4 (9 \frac{x}{4} - 5)}$

Step 2

Apply the distributive property.

$\frac{4 \frac{x}{4} + 4 \cdot - 3}{4 (9 \frac{x}{4}) + 4 \cdot - 5}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Cancel the common factor.

$\frac{4 \frac{x}{4} + 4 \cdot - 3}{4 (9 \frac{x}{4}) + 4 \cdot - 5}$

Step 3.1.2

Rewrite the expression.

$\frac{x + 4 \cdot - 3}{4 (9 \frac{x}{4}) + 4 \cdot - 5}$

Step 3.2

Multiply $4$ by $- 3$ .

$\frac{x - 12}{4 \cdot 9 \frac{x}{4} + 4 \cdot - 5}$

Step 4

Simplify the denominator.

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Step 4.1

Factor $4$ out of $4 \cdot 9 \frac{x}{4} + 4 \cdot - 5$ .

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Step 4.1.1

Factor $4$ out of $4 \cdot 9 \frac{x}{4}$ .

$\frac{x - 12}{4 (9 \frac{x}{4}) + 4 \cdot - 5}$

Step 4.1.2

Factor $4$ out of $4 \cdot - 5$ .

$\frac{x - 12}{4 (9 \frac{x}{4}) + 4 (- 5)}$

Step 4.1.3

Factor $4$ out of $4 (9 \frac{x}{4}) + 4 (- 5)$ .

$\frac{x - 12}{4 (9 \frac{x}{4} - 5)}$

Step 4.2

Combine $9$ and $\frac{x}{4}$ .

$\frac{x - 12}{4 (\frac{9 x}{4} - 5)}$

Step 4.3

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x - 12}{4 (\frac{9 x}{4} - 5 \cdot \frac{4}{4})}$

Step 4.4

Combine $- 5$ and $\frac{4}{4}$ .

$\frac{x - 12}{4 (\frac{9 x}{4} + \frac{- 5 \cdot 4}{4})}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{x - 12}{4 \frac{9 x - 5 \cdot 4}{4}}$

Step 4.6

Multiply $- 5$ by $4$ .

$\frac{x - 12}{4 \frac{9 x - 20}{4}}$

Step 5

Combine $4$ and $\frac{9 x - 20}{4}$ .

$\frac{x - 12}{\frac{4 (9 x - 20)}{4}}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Reduce the expression $\frac{4 (9 x - 20)}{4}$ by cancelling the common factors.

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Step 6.1.1

Cancel the common factor.

$\frac{x - 12}{\frac{4 (9 x - 20)}{4}}$

Step 6.1.2

Rewrite the expression.

$\frac{x - 12}{\frac{9 x - 20}{1}}$

Step 6.2

Divide $9 x - 20$ by $1$ .

$\frac{x - 12}{9 x - 20}$