SOLUTION: simplify the following by choosing which answer matches the problem. please show work. thank you. 2 5 [A] 7x+27 [B] 7 [C] 7 [D] 7x+27 --- + ---

Algebra ->  Functions -> SOLUTION: simplify the following by choosing which answer matches the problem. please show work. thank you. 2 5 [A] 7x+27 [B] 7 [C] 7 [D] 7x+27 --- + ---       Log On


   

Question 169732This question is from textbook intermediate algebra
: simplify the following by choosing which answer matches the problem. please show work. thank you.
2 5 [A] 7x+27 [B] 7 [C] 7 [D] 7x+27
--- + --- ----- ----- ----- ------
x+9 x-9 7 x+9 x^2-81 x^2-81

please help me with this problem. thank you! This question is from textbook intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how the LCD is %28x%2B9%29%28x-9%29. So we need to get EVERY denominator equal to the LCD.


2%2F%28x%2B9%29%2B5%2F%28x-9%29 Start with the given expression


%282%28x-9%29%29%2F%28%28x%2B9%29%28x-9%29%29%2B5%2F%28x-9%29 Multiply the first fraction by %28x-9%29%2F%28x-9%29


Multiply the second fraction by %28x%2B9%29%2F%28x%2B9%29


%282x-18%29%2F%28%28x%2B9%29%28x-9%29%29%2B%285x%2B45%29%2F%28%28x%2B9%29%28x-9%29%29 Distribute


%282x-18%29%2F%28x%5E2-81%29%2B%285x%2B45%29%2F%28x%5E2-81%29 FOIL


%282x-18%2B5x%2B45%29%2F%28x%5E2-81%29 Combine the fractions. This is possible since the denominators are equal.


%287x%2B27%29%2F%28x%5E2-81%29 Combine like terms.


So 2%2F%28x%2B9%29%2B5%2F%28x-9%29=%287x%2B27%29%2F%28x%5E2-81%29 where x%3C%3E-9 or x%3C%3E9


So the answer is choice D