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

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

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

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

Write each expression with a common denominator of $2 (x - 5)$ , by multiplying each by an appropriate factor of $1$ .

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

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

Reorder the factors of $(x - 5) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $- 1$ .

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