Simplify (5(x/4)-1)/(9(x/4)-4)

$\frac{5 (\frac{x}{4}) - 1}{9 (\frac{x}{4}) - 4}$

Step 1

Simplify the numerator.

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

$\frac{\frac{5 x}{4} - 1}{9 \frac{x}{4} - 4}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{5 x}{4} - 1 \cdot \frac{4}{4}}{9 \frac{x}{4} - 4}$

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{\frac{5 x}{4} + \frac{- 1 \cdot 4}{4}}{9 \frac{x}{4} - 4}$

Combine the numerators over the common denominator.

$\frac{\frac{5 x - 1 \cdot 4}{4}}{9 \frac{x}{4} - 4}$

Multiply $- 1$ by $4$ .

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

Step 2

Simplify the denominator.

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Multiply $- 4$ by $4$ .

$\frac{\frac{5 x - 4}{4}}{\frac{9 x - 16}{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 x - 4}{4} \cdot \frac{4}{9 x - 16}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5 x - 4}{4} \cdot \frac{4}{9 x - 16}$

Rewrite the expression.

$(5 x - 4) \frac{1}{9 x - 16}$

Step 5

Multiply $5 x - 4$ by $\frac{1}{9 x - 16}$ .

$\frac{5 x - 4}{9 x - 16}$