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

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

Step 1

To write $\frac{3}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x + 4}{x + 4}$ .

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

Step 2

Simplify terms.

Multiply $\frac{3}{x + 3}$ by $\frac{x + 4}{x + 4}$ .

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

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $4$ .

$\frac{3 x + 12 - 2 x}{(x + 3) (x + 4)}$

Subtract $2 x$ from $3 x$ .

$\frac{x + 12}{(x + 3) (x + 4)}$