Question

4x/ 2x + y + 2y/ 2x + y Perform the indicated operation. Be sure the answer is reduced.

Answer 1

Answer:

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

Step-by-step explanation:

Given:

The expression to simplify is given as:

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

Since, the denominator is same, we add the numerators and divide it by the same denominator. This gives,

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

Now, we simplify further by factoring out the common terms from the numerator and denominator if possible.

We observe that, 2 is a common factor to both $4x\ and\ 2y$. So, we factor out 2 from the numerator. This gives,

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

Now, the term $2x+y$ is common in both the numerator and denominator. Hence, $\frac{2x+y}{2x+y}=1$

So, the simplified form is:

$=2\times \frac{2x+y}{2x+y}\\\\=2\times 1\\\\=2$