Simplify 3/(x+3)-(2x)/((x+3)(x+1))

$\frac{3}{x + 3} - \frac{2 x}{(x + 3) (x + 1)}$

Step 1

To write $\frac{3}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{3}{x + 3} \cdot \frac{x + 1}{x + 1} - \frac{2 x}{(x + 3) (x + 1)}$

Step 2

Simplify terms.

Multiply $\frac{3}{x + 3}$ by $\frac{x + 1}{x + 1}$ .

$\frac{3 (x + 1)}{(x + 3) (x + 1)} - \frac{2 x}{(x + 3) (x + 1)}$

Combine the numerators over the common denominator.

$\frac{3 (x + 1) - 2 x}{(x + 3) (x + 1)}$

Step 3

Simplify the numerator.

Apply the distributive property.

$\frac{3 x + 3 \cdot 1 - 2 x}{(x + 3) (x + 1)}$

Multiply $3$ by $1$ .

$\frac{3 x + 3 - 2 x}{(x + 3) (x + 1)}$

Subtract $2 x$ from $3 x$ .

$\frac{x + 3}{(x + 3) (x + 1)}$

Step 4

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{x + 3}{(x + 3) (x + 1)}$

Rewrite the expression.

$\frac{1}{x + 1}$