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

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(75887) (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(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Factor to get .

Factor to get .

Factor to get .

Combine the fractions.

Highlight the common terms.

Cancel out the common terms.

Simplify.

So simplifies to .

In other words, where ,, or

So the answer choice is C
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