SOLUTION: 8/x+3 + 9/x-3

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Question 151283: 8/x+3 + 9/x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%288%29%2F%28x%2B3%29%2B%289%29%2F%28x-3%29 Start with the given expression

Now let's find the LCM of the denominators %28x%2B3%29 and %28x-3%29. It turns out that the LCM of these denominators is %28x%2B3%29%28x-3%29. So the goal is to get both denominators to the LCD %28x%2B3%29%28x-3%29


Multiply the 1st fraction by %28%28x-3%29%29%2F%28%28x-3%29%29



Combine the fractions.


Multiply the 2nd fraction by %28%28x%2B3%29%29%2F%28%28x%2B3%29%29


Combine the fractions.


%288x-24%29%2F%28%28x%2B3%29%28x-3%29%29%2B%289x%2B27%29%2F%28%28x%2B3%29%28x-3%29%29 Distribute


%288x-24%2B9x%2B27%29%2F%28%28x%2B3%29%28x-3%29%29 Add the fractions. This is now possible since both denominators are equal.


%2817x%2B3%29%2F%28%28x%2B3%29%28x-3%29%29 Combine like terms.


%2817x%2B3%29%2F%28x%5E2-9%29 FOIL


So %288%29%2F%28x%2B3%29%2B%289%29%2F%28x-3%29 simplifies to %2817x%2B3%29%2F%28x%5E2-9%29


In other words, %288%29%2F%28x%2B3%29%2B%289%29%2F%28x-3%29=%2817x%2B3%29%2F%28x%5E2-9%29 where x%3C%3E-3 or x%3C%3E3