SOLUTION: Can you please exlpain step by step how to solve 2/x-3 - 4/x+3 = 8/x^2-9

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please exlpain step by step how to solve 2/x-3 - 4/x+3 = 8/x^2-9      Log On


   

Question 582488: Can you please exlpain step by step how to solve 2/x-3 - 4/x+3 = 8/x^2-9
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28x-3%29+-+4%2F%28x%2B3%29 = 8%2F%28x%5E2-9%29
The third denominator is the difference of squares and can be factored to;
2%2F%28x-3%29+-+4%2F%28x%2B3%29 = 8%2F%28%28x-3%29%28x%2B3%29%29
Multiply each term by (x-3)(x+3)
(x-3)(x+3)*2%2F%28x-3%29 - (x-3)(x+3)*4%2F%28x%2B3%29 = (x-3)(x+3)*8%2F%28%28x-3%29%28x%2B3%29%29
Cancel the denominators and you have:
2(x+3) - 4(x-3) = 8
2x + 6 - 4x + 12 = 8
2x - 4x + 18 = 8
-2x = 8 - 18
-2x = -10
x = +5
:
:
Check this in the original problem for x = 5
2%2F%285-3%29+-+4%2F%285%2B3%29 = 8%2F%285%5E2-9%29