SOLUTION: 3x+6 over 4x+12 DIVIDED BY x^2-4 over x+3

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Question 252593: 3x+6 over 4x+12 DIVIDED BY x^2-4 over x+3
Found 2 solutions by drk, jim_thompson5910:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the original problem:
%283x%2B6%29+%2F++%284x%2B12%29 / %28x%5E2-4%29+%2F+%28x%2B3%29
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step 1 - factor everything you can and then flip the second fraction and change to multiplication. We get
3%28x%2B2%29+%2F+4%28x%2B3%29 * %28x%2B3%29+%2F+%28x%2B2%29%28x-2%29
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step 2 - cancel what you can. We get
3%2F4+%2A+1%2F%28x-2%29
which is:
3 / (4x-8)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%283x%2B6%29%2F%284x%2B12%29%29%2F%28%28x%5E2-4%29%2F%28x%2B3%29%29 Start with the given expression.


%28%283x%2B6%29%2F%284x%2B12%29%29%28%28x%2B3%29%2F%28x%5E2-4%29%29 Multiply the first fraction %283x%2B6%29%2F%284x%2B12%29 by the reciprocal of the second fraction %28x%5E2-4%29%2F%28x%2B3%29.


%28%283%28x%2B2%29%29%2F%284x%2B12%29%29%28%28x%2B3%29%2F%28x%5E2-4%29%29 Factor 3x%2B6 to get 3%28x%2B2%29.


%28%283%28x%2B2%29%29%2F%284%28x%2B3%29%29%29%28%28x%2B3%29%2F%28x%5E2-4%29%29 Factor 4x%2B12 to get 4%28x%2B3%29.


%28%283%28x%2B2%29%29%2F%284%28x%2B3%29%29%29%28%28x%2B3%29%2F%28%28x-2%29%28x%2B2%29%29%29 Factor x%5E2-4 to get %28x-2%29%2A%28x%2B2%29.


%283%28x%2B2%29%28x%2B3%29%29%2F%284%28x%2B3%29%28x-2%29%28x%2B2%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


3%2F%284%28x-2%29%29 Simplify.


3%2F%284x-8%29 Distribute.


So %28%283x%2B6%29%2F%284x%2B12%29%29%2F%28%28x%5E2-4%29%2F%28x%2B3%29%29 simplifies to 3%2F%284x-8%29.


In other words, %28%283x%2B6%29%2F%284x%2B12%29%29%2F%28%28x%5E2-4%29%2F%28x%2B3%29%29=3%2F%284x-8%29