For this case we must indicate an expression equivalent to:
[tex]x + 2 + [4x- \frac {x ^ 2 + 6x + 8} {x + 4}][/tex]
If we factor the quadratic expression, we must find two numbers that when multiplied give as result 8, and when summed give as result 6. These numbers are 4 and 2. Then:
[tex]x ^ 2 + 6x + 8 = (x + 2) (x + 4)[/tex]
Rewriting the expression:
[tex]x + 2 + [4x- \frac {(x + 2) (x + 4)} {(x + 4)}] =[/tex]
Simplifying common terms we have:
[tex]x + 2 + [4x- (x + 2)] =[/tex]
Taking into account that:
[tex]- * + = -\\x + 2 + 4x-x-2 =\\x-x + 2-2 + 4x =\\4x[/tex]
ANswer:
4x
