SOLUTION: B 2b ----+---- b-1 b squared - 1

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Question 153182: B 2b
----+----
b-1 b squared - 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
b%2F%28b-1%29%2B%282b%29%2F%28b%5E2-1%29 Start with the given expression.


b%2F%28b-1%29%2B%282b%29%2F%28%28b-1%29%28b%2B1%29%29 Factor b%5E2-1 to get %28b-1%29%28b%2B1%29. Notice how the LCD is %28b-1%29%28b%2B1%29


%28%28b%2B1%29%2F%28b%2B1%29%29%28b%2F%28b-1%29%29%2B%282b%29%2F%28%28b-1%29%28b%2B1%29%29 Multiply the first term by %28b%2B1%29%2F%28b%2B1%29. The goal is to get the first denominator equal to the LCD %28b-1%29%28b%2B1%29


%28b%28b%2B1%29%29%2F%28%28b-1%29%28b%2B1%29%29%2B%282b%29%2F%28%28b-1%29%28b%2B1%29%29 Combine the fractions.


%28b%5E2%2Bb%29%2F%28%28b-1%29%28b%2B1%29%29%2B%282b%29%2F%28%28b-1%29%28b%2B1%29%29 Distribute


%28b%5E2%2Bb%2B2b%29%2F%28%28b-1%29%28b%2B1%29%29 Add the fractions.


%28b%5E2%2B3b%29%2F%28%28b-1%29%28b%2B1%29%29 Combine like terms.


So b%2F%28b-1%29%2B%282b%29%2F%28b%5E2-1%29=%28b%5E2%2B3b%29%2F%28%28b-1%29%28b%2B1%29%29 where b%3C%3E-1 or b%3C%3E1