SOLUTION: Please perform the indicated operation: (x / (x^2 - 9)) - ((x + 1) / (x^2 + 6*x + 9))

Algebra ->  Rational-functions -> SOLUTION: Please perform the indicated operation: (x / (x^2 - 9)) - ((x + 1) / (x^2 + 6*x + 9))      Log On


   

Question 971105: Please perform the indicated operation:
(x / (x^2 - 9)) - ((x + 1) / (x^2 + 6*x + 9))
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%5E2-9%29-%28x%2B1%29%2F%28x%5E2%2B6x%2B9%29

1). Find the LCD of both fractions: x%5E2-9 can be factored as %28x%2B3%29%28x-3%29
X%5E2%2B6x%2B9 can be factored as %28x%2B3%29%5E2

2). Replace the denominators of each fraction with %28x%2B3%29%5E2%2A%28x-3%29:

x%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29-%28x%2B1%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29

3). Multiply the numerator of fraction #1 by x%2B3:

%28x%28x%2B3%29%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29 -----> %28x%5E2%2B3x%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29

4). Multiply the numerator of fraction #2 by x-3:

%28%28x%2B1%29%28x-3%29%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29 -----> %28x%5E2-2x-3%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29

5). Subtract numerator of fraction #2 from fraction #1 numerator:

%28x%5E2%2B3x-x%5E2%2B2x%2B3%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29 -----> %285x%2B3%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29

Final Answer: %285x%2B3%29%2F%28%28x%2B3%29%5E2%2A%28x-3%29%29