SOLUTION: Rational Expression: 4/a^2 - 1 + 1/2a + 2

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Question 97207: Rational Expression:
4/a^2 - 1 + 1/2a + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%28a%5E2+-+1%29++%2B++1%2F%282a+%2B+2%29 Start with the given expression


4%2F%28a%2B1%29%28a-1%29++%2B++1%2F%282a+%2B+2%29 Factor a%5E2-1 to %28a%2B1%29%28a-1%29


4%2F%28a%2B1%29%28a-1%29++%2B++1%2F2%28a+%2B+1%29 Factor 2a%2B2 to 2%28a%2B1%29


So our LCD is 2%28a%2B1%29%28a-1%29 (this is what we want the denominators to get to)


%282%2F2%29%284%2F%28a%2B1%29%28a-1%29%29++%2B++1%2F2%28a+%2B+1%29 Multiply the first fraction by 2%2F2

Multiply the second fraction by %28a-1%29%2F%28a-1%29


%288%2F2%28a%2B1%29%28a-1%29%29++%2B++%28%28a-1%29%2F2%28a+%2B+1%29%28a-1%29%29 Multiply


%288%2Ba-1%29%2F2%28a+%2B+1%29%28a-1%29 Combine the fractions. We can do this since the denominators are the same.

%287%2Ba%29%2F2%28a+%2B+1%29%28a-1%29 Combine like terms