Question

Which expression is equivalent to?

Answer 1

`4x`

Explanation:

The given expression is

`x+2+[4x-(x^2+6x+8)/(x+4) ]`

Let us first of all split the middle term of the quadratic trinomial to get,

`=x+2+[4x-(x^2+2x+4x+8)/(x+4) ]`

We simplify to get;

`=x+2+[4x-(x(x+2)+4(x+2))/(x+4) ]`

We factor to obatin,

`=x+2+[4x-((x+2)(x+4))/(x+4) ]`

We cancel the common factor to get,

`=x+2+[4x-(x+2)]`

This simplifies to,

`=x+2+4x-x-2`

This gives us,

`=4x`

Answer 2

4x

steps

`x+2 + (4x-(x^2+6x+8)/(x+4) )`

factor x^2 + 6x + 8

product=8 and sum =6

4 times 2 = 8

4 + 2= 6

(x+4)(x+2)

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

Cancel out x+4 at the top and bottom

x + 2 +(4x -(x+2))

Now we remove the parenthesis

x + 2+4x -x-2

4x

So the final answer is 4x