SOLUTION: i need help with the following problem: solve for x: x/x+5 - 5/x-5= x^2+25/x^2-25 find LCM of: x^2+8x+16 and x^2+x-12 im just not sure about the process? im not even reall

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i need help with the following problem: solve for x: x/x+5 - 5/x-5= x^2+25/x^2-25 find LCM of: x^2+8x+16 and x^2+x-12 im just not sure about the process? im not even reall      Log On


   

Question 537122: i need help with the following problem:
solve for x: x/x+5 - 5/x-5= x^2+25/x^2-25
find LCM of: x^2+8x+16 and x^2+x-12
im just not sure about the process? im not even really sure how to start.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
x%2F%28x%2B5%29-5%2F%28x-5%29+=+%28x%5E2%2B25%29%2F%28x%5E2-25%29 I would first add the two fractions on the left side using the LCD of %28x%2B5%29%28x-5%29
Simplify the left side.
%28x%5E2-5x-5x-25%29%2F%28x%2B5%29%28x-5%29+=+%28x%5E2%2B25%29%2F%28x%5E2-25%29 Now factor the denominator on the right side.
%28x%5E2-10x-25%29%2F%28x%2B5%29%28x-5%29+=+%28x%5E2%2B25%29%2F%28x%2B5%29%28x-5%29 Multiply both sides by %28x%2B5%29%28x-5%29.
x%5E2-10x-25+=+x%5E2%2B25 Subtract x%5E2 from both sides.
-10x-25+=+25 Add 25 to both sides.
-10x+=+50 Finally, divide both sides by -10.
highlight%28x+=+-5%29
However, when you try to check this solution by substituting x+=+-5 in the original equation, you will have division by zero in two of the terms, which means that this solution is invalid.
This equation, therefore, has no solution!