Simplify (3(x/2)-5)/((x/2)-4)

$\frac{3 (\frac{x}{2}) - 5}{(\frac{x}{2}) - 4}$

Multiply the numerator and denominator of the complex fraction by $2$ .

Multiply $\frac{3 \frac{x}{2} - 5}{\frac{x}{2} - 4}$ by $\frac{2}{2}$ .

$\frac{2}{2} \cdot \frac{3 \frac{x}{2} - 5}{\frac{x}{2} - 4}$

Combine.

$\frac{2 (3 \frac{x}{2} - 5)}{2 (\frac{x}{2} - 4)}$

Apply the distributive property.

$\frac{2 (3 \frac{x}{2}) + 2 \cdot - 5}{2 \frac{x}{2} + 2 \cdot - 4}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (3 \frac{x}{2}) + 2 \cdot - 5}{2 \frac{x}{2} + 2 \cdot - 4}$

Rewrite the expression.

$\frac{2 (3 \frac{x}{2}) + 2 \cdot - 5}{x + 2 \cdot - 4}$

Simplify the numerator.

Factor $2$ out of $2 \cdot 3 \frac{x}{2} + 2 \cdot - 5$ .

Factor $2$ out of $2 \cdot 3 \frac{x}{2}$ .

$\frac{2 (3 \frac{x}{2}) + 2 \cdot - 5}{x + 2 \cdot - 4}$

Factor $2$ out of $2 \cdot - 5$ .

$\frac{2 (3 \frac{x}{2}) + 2 (- 5)}{x + 2 \cdot - 4}$

Factor $2$ out of $2 (3 \frac{x}{2}) + 2 (- 5)$ .

$\frac{2 (3 \frac{x}{2} - 5)}{x + 2 \cdot - 4}$

Combine $3$ and $\frac{x}{2}$ .

$\frac{2 (\frac{3 x}{2} - 5)}{x + 2 \cdot - 4}$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 (\frac{3 x}{2} - 5 \cdot \frac{2}{2})}{x + 2 \cdot - 4}$

Combine $- 5$ and $\frac{2}{2}$ .

$\frac{2 (\frac{3 x}{2} + \frac{- 5 \cdot 2}{2})}{x + 2 \cdot - 4}$

Combine the numerators over the common denominator.

$\frac{2 \frac{3 x - 5 \cdot 2}{2}}{x + 2 \cdot - 4}$

Multiply $- 5$ by $2$ .

$\frac{2 \frac{3 x - 10}{2}}{x + 2 \cdot - 4}$

Combine fractions.

Multiply $2$ by $- 4$ .

$\frac{2 \frac{3 x - 10}{2}}{x - 8}$

Combine $2$ and $\frac{3 x - 10}{2}$ .

$\frac{\frac{2 (3 x - 10)}{2}}{x - 8}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{2 (3 x - 10)}{2}$ by cancelling the common factors.

Cancel the common factor.

$\frac{\frac{2 (3 x - 10)}{2}}{x - 8}$

Rewrite the expression.

$\frac{\frac{3 x - 10}{1}}{x - 8}$

Divide $3 x - 10$ by $1$ .

$\frac{3 x - 10}{x - 8}$