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

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

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

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $2 y$ .

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

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

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

Step 3

Cancel the common factor of $2 x + y$ .

Cancel the common factor.

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

Divide $2$ by $1$ .

$2$