SOLUTION: Solve {{{1/(4x+12)-1/(x^2-9)=5/(x-3)}}}

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Question 143036: Solve 1%2F%284x%2B12%29-1%2F%28x%5E2-9%29=5%2F%28x-3%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%284x%2B12%29-1%2F%28x%5E2-9%29=5%2F%28x-3%29 Start with the given equation


1%2F%284%28x%2B3%29%29-1%2F%28%28x-3%29%28x%2B3%29%29=5%2F%28x-3%29 Factor 4x%2B12 to get 4%28x%2B3%29. Factor x%5E2-9 to get %28x-3%29%28x%2B3%29


So the LCD is 4%28x%2B3%29%28x-3%29


Multiply both sides by the LCD 4%28x%2B3%29%28x-3%29 to clear the fractions


%28x-3%29-4=20%28x%2B3%29 Distribute and multiply


x-3-4=20x%2B60 Distribute again


x-7=20x%2B60 Combine like terms on the left side


x=20x%2B60%2B7Add 7 to both sides


x-20x=60%2B7 Subtract 20x from both sides


-19x=60%2B7 Combine like terms on the left side


-19x=67 Combine like terms on the right side


x=%2867%29%2F%28-19%29 Divide both sides by -19 to isolate x



x=-67%2F19 Reduce

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Answer:
So our answer is x=-67%2F19 (which is approximately x=-3.5263 in decimal form)