SOLUTION: Can someone please help. I am confused. x/x+8-8/x-8=x^2+64/x^-64

Algebra ->  Equations -> SOLUTION: Can someone please help. I am confused. x/x+8-8/x-8=x^2+64/x^-64      Log On


   

Question 127397: Can someone please help. I am confused.
x/x+8-8/x-8=x^2+64/x^-64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%2B8%29-8%2F%28x-8%29=%28x%5E2%2B64%29%2F%28x%5E2-64%29 Start with the given equation


x%2F%28x%2B8%29-8%2F%28x-8%29=%28x%5E2%2B64%29%2F%28%28x%2B8%29%28x-8%29%29 Factor x%5E2-64 to get %28x%2B8%29%28x-8%29

Here we can see that the LCD is %28x%2B8%29%28x-8%29

Multiply both sides by the LCD %28x%2B8%29%28x-8%29. This will eliminate the fractions


x%28x-8%29-8%28x%2B8%29=x%5E2%2B64 Distribute and multiply


x%5E2-8x-8x-64=x%5E2%2B64 Distribute again


x%5E2-8x-8x-64-x%5E2-64=0 Subtract x%5E2 from both sides. Subtract 64 from both sides.


16x-128=0 Combine like terms


16x=128 Add 128 to both sides


x=%28128%29%2F%2816%29 Divide both sides by 16 to isolate x



x=8 Divide



So the possible answer is x=8



Check:


Now let's plug in x=8 into x%2F%28x%2B8%29-8%2F%28x-8%29=%28x%5E2%2B64%29%2F%28x%5E2-64%29


x%2F%28x%2B8%29-8%2F%28x-8%29=%28x%5E2%2B64%29%2F%28x%5E2-64%29 Start with the given equation


8%2F%288%2B8%29-8%2F%288-8%29=%28x%5E2%2B64%29%2F%288%5E2-64%29 Plug in x=8


8%2F16-8%2F0=%28x%5E2%2B64%29%2F0 Combine like terms


Since we have zero denominators, the possible solution x=8 is not a solution.



So there are no solutions.