Question

Which expression is equivalent to?

Answer 1

answer

4x

steps

$x+2 + (4x-\frac{x^2+6x+8}{x+4} )$

factor x^2 + 6x + 8

product=8 and sum =6

4 times 2 = 8

4 + 2= 6

(x+4)(x+2)

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

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

Answer 2

Answer:

$4x$

Step-by-step explanation:

The given expression is

$x+2+[4x-\frac{x^2+6x+8}{x+4} ]$

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

$=x+2+[4x-\frac{x^2+2x+4x+8}{x+4} ]$

We simplify to get;

$=x+2+[4x-\frac{x(x+2)+4(x+2)}{x+4} ]$

We factor to obatin,

$=x+2+[4x-\frac{(x+2)(x+4)}{x+4} ]$

We cancel the common factor to get,

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

This simplifies to,

$=x+2+4x-x-2$

This gives us,

$=4x$