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

$\frac{3 x}{x + 2} + \frac{x}{x + 4}$

To write $\frac{3 x}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x + 4}{x + 4}$ .

$\frac{3 x}{x + 2} \cdot \frac{x + 4}{x + 4} + \frac{x}{x + 4}$

To write $\frac{x}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{3 x}{x + 2} \cdot \frac{x + 4}{x + 4} + \frac{x}{x + 4} \cdot \frac{x + 2}{x + 2}$

Write each expression with a common denominator of $(x + 2) (x + 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{x + 2}$ by $\frac{x + 4}{x + 4}$ .

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

Multiply $\frac{x}{x + 4}$ by $\frac{x + 2}{x + 2}$ .

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

Reorder the factors of $(x + 4) (x + 2)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x (x + 4) + x (x + 2)$ .

Factor $x$ out of $3 x (x + 4)$ .

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

Factor $x$ out of $x (3 (x + 4)) + x (x + 2)$ .

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

Apply the distributive property.

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

Multiply $3$ by $4$ .

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

Add $3 x$ and $x$ .

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

Add $12$ and $2$ .

$\frac{x (4 x + 14)}{(x + 2) (x + 4)}$

Factor $2$ out of $4 x + 14$ .

Factor $2$ out of $4 x$ .

$\frac{x (2 (2 x) + 14)}{(x + 2) (x + 4)}$

Factor $2$ out of $14$ .

$\frac{x (2 (2 x) + 2 (7))}{(x + 2) (x + 4)}$

Factor $2$ out of $2 (2 x) + 2 (7)$ .

$\frac{x (2 (2 x + 7))}{(x + 2) (x + 4)}$

$\frac{x \cdot 2 (2 x + 7)}{(x + 2) (x + 4)}$

Move $2$ to the left of $x$ .

$\frac{2 x (2 x + 7)}{(x + 2) (x + 4)}$