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

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

Step 1

Simplify the numerator.

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Multiply $- 4$ by $4$ .

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

Step 2

Simplify the denominator.

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

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

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

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

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

$\frac{\frac{9 x - 16}{4}}{\frac{5 x}{4} + \frac{- 1 \cdot 4}{4}}$

Combine the numerators over the common denominator.

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

Multiply $- 1$ by $4$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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