SOLUTION: Hi,I am having a hard time with this equation and would like some help.{{{x+4}}}/{{{x^2+8x+16}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi,I am having a hard time with this equation and would like some help.{{{x+4}}}/{{{x^2+8x+16}}}      Log On


   

Question 310385: Hi,I am having a hard time with this equation and would like some help.x%2B4/x%5E2%2B8x%2B16
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B4/x%5E2%2B8x%2B16

Factoring is tricky but don't let it intimidate you. Just do this:

%28x+%2B+4%29%2F%28x+%2B+4%29%28x+%2B+4%29

Now can you see that these highlighted terms cancel each other?
%28highlight%28x+%2B+4%29%29%2F%28highlight%28x+%2B+4%29%29%28x+%2B+4%29

BUT when I say: "cancel" I'm not meaning that you can just just wipe out the (x + 4) in the numerator. Why? Well, when we "cancel" terms, we aren't just DELETING them! Think of this: 4%2F4 = 1, right? Similarly, 25%2F25 = 1, right?


SO when we cancel out the (x + 4) above, we are really saying that %28x+%2B+4%29%2F%28x+%2B+4%29 equals 1.


Therefore, this: %28highlight%28x+%2B+4%29%29%2F%28highlight%28x+%2B+4%29%29%28x+%2B+4%29

is really: %281%29%2F%28x+%2B+4%29

Does that make sense? I hope so. If you need more help with canceling and factoring, check out my YouTube videos. Just do a search on YouTube for PRMathChicago and when you find my name, you'll see some vids that my help you because they explain this in more detail.

Good luck. :-)