SOLUTION: Perform the indicated operations and simplify the following expression: x+6/x^2-16 * 3x-12/3x+18 A) 0 B) 3 / 3(x+4) C) 1/x+4 D) -1/x+4

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Perform the indicated operations and simplify the following expression: x+6/x^2-16 * 3x-12/3x+18 A) 0 B) 3 / 3(x+4) C) 1/x+4 D) -1/x+4      Log On

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Question 145591: Perform the indicated operations and simplify the following expression:
x+6/x^2-16 * 3x-12/3x+18
A) 0
B) 3 / 3(x+4)
C) 1/x+4
D) -1/x+4
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the indicated operations and simplify the following expression:
[(x+6)/(x^2-16)] * [(3x-12)/(3x+18)]
Factor where you can to get:
[(x+6)/[(x-4)(x+4)]] * [3(x-4)/[3(x+6)]
Cancel any fact that is common to numerator and a denominator
such as (x+6) and (x-4) and 3
-------
= [1/[(x+4)]] * [1/[1])]
= 1/(x+4)
============
Cheers,
Stan H.
A) 0
B) 3 / 3(x+4)
C) 1/x+4
D) -1/x+4

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%2B6%29%2F%28x%5E2-16%29%29%28%283x-12%29%2F%283x%2B18%29%29 Start with the given expression.



%28%28x%2B6%29%2F%28%28x-4%29%2A%28x%2B4%29%29%29%28%283x-12%29%2F%283x%2B18%29%29 Factor x%5E2-16 to get %28x-4%29%2A%28x%2B4%29.


%28%28x%2B6%29%2F%28%28x-4%29%2A%28x%2B4%29%29%29%28%283%28x-4%29%29%2F%283x%2B18%29%29 Factor 3x-12 to get 3%28x-4%29.


%28%28x%2B6%29%2F%28%28x-4%29%2A%28x%2B4%29%29%29%28%283%28x-4%29%29%2F%283%28x%2B6%29%29%29 Factor 3x%2B18 to get 3%28x%2B6%29.


%283%28x%2B6%29%28x-4%29%29%2F%283%28x-4%29%28x%2B4%29%28x%2B6%29%29 Combine the fractions.


%28highlight%283%29highlight%28x%2B6%29highlight%28x-4%29%29%2F%28highlight%283%29highlight%28x-4%29%28x%2B4%29highlight%28x%2B6%29%29 Highlight the common terms.


%28cross%283%29cross%28x%2B6%29cross%28x-4%29%29%2F%28cross%283%29cross%28x-4%29%28x%2B4%29cross%28x%2B6%29%29 Cancel out the common terms.


%281%29%2F%28%28x%2B4%29%29 Simplify.


So %28%28x%2B6%29%2F%28x%5E2-16%29%29%28%283x-12%29%2F%283x%2B18%29%29 simplifies to %281%29%2F%28%28x%2B4%29%29.


In other words, %28%28x%2B6%29%2F%28x%5E2-16%29%29%28%283x-12%29%2F%283x%2B18%29%29=%281%29%2F%28%28x%2B4%29%29 where x%3C%3E-4,x%3C%3E4, or x%3C%3E-6



So the answer choice is C