Question

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

Answer 1

`(4x)/(2x+y) +(2y)/(2x+y)=2`

Explanation:

Given:

The expression to simplify is given as:

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

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

`(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,

`(2(2x+y))/(2x+y)`

Now, the term
`2x+y` is common in both the numerator and denominator. Hence,
`(2x+y)/(2x+y)=1`

So, the simplified form is:

`=2* (2x+y)/(2x+y)\\\\=2* 1\\\\=2`