SOLUTION: Solve {{{4-(a-2)/(a+5)=(a^2-18)/(a+5)}}}

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Question 125833: Solve

4-%28a-2%29%2F%28a%2B5%29=%28a%5E2-18%29%2F%28a%2B5%29
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
4-%28a-2%29%2F%28a%2B5%29=%28a%5E2-18%29%2F%28a%2B5%29 Start with the given equation


%28a%2B5%29%284-%28a-2%29%2F%28cross%28a%2B5%29%29%29=cross%28a%2B5%29%28%28a%5E2-18%29%2F%28cross%28a%2B5%29%29%29 Multiply both sides by the LCD %28a%2B5%29. Doing this will eliminate every fraction.


%28a%2B5%29%284%29-%28a-2%29=a%5E2-18 Distribute and multiply. Notice every denominator has been canceled out.


4%28a%2B5%29-%28a-2%29=a%5E2-18 Rearrange the terms


4a%2B20-a%2B2=a%5E2-18 Distribute


3a%2B22=a%5E2-18 Combine like terms


3a%2B22-a%5E2%2B18=0 Subtract a^2 from both sides. Add 18 to both sides.


-a%5E2%2B3a%2B40=0 Combine like terms


%28-a%2B8%29%28a%2B5%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
-a%2B8=0 or a%2B5=0

a=8 or a=-5 Now solve for a in each case


So our possible answers are
a=8 or a=-5



However, if you plug in a=-5 into the original equation 4-%28a-2%29%2F%28a%2B5%29=%28a%5E2-18%29%2F%28a%2B5%29, you'll get a denominator of zero. So a=-5 is not a solution since a=-5 is not in the domain.



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Answer:

So the only solution is

a=8