SOLUTION: For all x ≠ –4, which of the following is equivalent to the expression below? x2 + 12x + 32 / x + 4 A. x + 3 B. x + 8 C. x + 11 D. x + 16 E. x + 28 -----------

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For all x ≠ –4, which of the following is equivalent to the expression below? x2 + 12x + 32 / x + 4 A. x + 3 B. x + 8 C. x + 11 D. x + 16 E. x + 28 -----------      Log On


   

Question 303793: For all x ≠ –4, which of the following is equivalent to the expression below?
x2 + 12x + 32 / x + 4

A. x + 3
B. x + 8
C. x + 11
D. x + 16
E. x + 28
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this question came from ACT practice test and it says that this problem is a type of rational expression. However, I checked the rational expression chapter on my old algebra book and I don't see any lessons on how to solve this kind of problem. Therefore, if you could tell me what kind of problem this is so I can do more practice questions online, i would really appreciate it. Thanks in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2B12x%2B32%29%2F%28x%2B4%29 Start with the given expression.


%28%28x%2B4%29%28x%2B8%29%29%2F%28x%2B4%29 Factor the numerator


%28highlight%28%28x%2B4%29%29%28x%2B8%29%29%2Fhighlight%28%28x%2B4%29%29 Highlight the common terms.


%28cross%28%28x%2B4%29%29%28x%2B8%29%29%2Fcross%28%28x%2B4%29%29 Cancel out the common terms.


x%2B8 Simplify.


So %28x%5E2%2B12x%2B32%29%2F%28x%2B4%29 simplifies to x%2B8 making the answer B.


In other words, %28x%5E2%2B12x%2B32%29%2F%28x%2B4%29=x%2B8 where x%3C%3E-4