Simplify 9/(2(x+3))-x/(x+3)

$\frac{9}{2 (x + 3)} - \frac{x}{x + 3}$

Step 1

To write $- \frac{x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2 (x + 3)} - \frac{x}{x + 3} \cdot \frac{2}{2}$

Step 2

Write each expression with a common denominator of $2 (x + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{x + 3}$ by $\frac{2}{2}$ .

$\frac{9}{2 (x + 3)} - \frac{x \cdot 2}{(x + 3) \cdot 2}$

Reorder the factors of $(x + 3) \cdot 2$ .

$\frac{9}{2 (x + 3)} - \frac{x \cdot 2}{2 (x + 3)}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 - x \cdot 2}{2 (x + 3)}$

Step 4

Multiply $2$ by $- 1$ .

$\frac{9 - 2 x}{2 (x + 3)}$