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

$\frac{3 x}{x + 3} + \frac{x}{x + 2}$

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

$\frac{3 x}{x + 3} \cdot \frac{x + 2}{x + 2} + \frac{x}{x + 2}$

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

$\frac{3 x}{x + 3} \cdot \frac{x + 2}{x + 2} + \frac{x}{x + 2} \cdot \frac{x + 3}{x + 3}$

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x (x + 2) + x (x + 3)$ .

Factor $x$ out of $3 x (x + 2)$ .

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

Factor $x$ out of $x (3 (x + 2)) + x (x + 3)$ .

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

Apply the distributive property.

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

Multiply $3$ by $2$ .

$\frac{x (3 x + 6 + x + 3)}{(x + 2) (x + 3)}$

Add $3 x$ and $x$ .

$\frac{x (4 x + 6 + 3)}{(x + 2) (x + 3)}$

Add $6$ and $3$ .

$\frac{x (4 x + 9)}{(x + 2) (x + 3)}$