SOLUTION: 16 2(x-4) --- + ------ x2-16 x+4 Adding Rational Expressions

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Question 145505: 16 2(x-4)
--- + ------
x2-16 x+4
Adding Rational Expressions
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29 Start with the given expression


%2816%29%2F%28%28x%2B4%29%28x-4%29%29%2B%282%28x-4%29%29%2F%28x%2B4%29 Factor x%5E2-16 to get %28x%2B4%29%28x-4%29. So the LCD is %28x%2B4%29%28x-4%29


Multiply the second fraction by %28x-4%29%2F%28x-4%29


Combine the fractions



%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%28x-4%29%29%2F%28x%5E2-16%29 Foil %28x%2B4%29%28x-4%29 to get x%5E2-16


%2816%29%2F%28x%5E2-16%29%2B%282%28x%5E2-8x%2B16%29%29%2F%28x%5E2-16%29 Foil %28x-4%29%28x-4%29 to get x%5E2-8x%2B16


%2816%29%2F%28x%5E2-16%29%2B%282x%5E2-16x%2B32%29%2F%28x%5E2-16%29 Distribute


%28%2816%29%2B%282x%5E2-16x%2B32%29%29%2F%28x%5E2-16%29 Since the two fractions have the same denominator, this means we can combine them.


%282x%5E2-16x%2B48%29%2F%28x%5E2-16%29 Combine like terms


So %2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29 simplifies to %282x%5E2-16x%2B48%29%2F%28x%5E2-16%29.


In other words, where x%3C%3E-4 or x%3C%3E4