SOLUTION: Could you please show me in detail this problem: 1/x + 6/y ___________ 1/x2 - 36/y2 Thank you very much!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Could you please show me in detail this problem: 1/x + 6/y ___________ 1/x2 - 36/y2 Thank you very much!      Log On


   

Question 92456: Could you please show me in detail this problem:
1/x + 6/y
___________
1/x2 - 36/y2
Thank you very much!
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please show me in detail this problem:
1/x + 6/y
___________
1/x2 - 36/y2
Thank you very much!
%28%281%2Fx%29%2B%286%2Fy%29%29%2F%28%281%2Fx%5E2%29-%2836%2Fy%5E2%29%29%29
Our approach will be to first simplify the numerator and then simplify the denominator and finally put them back together and simplify again.
Numerator:
%281%2Fx%29%2B%286%2Fy%29 multiply each term by xy%2Fxy and we get
%28y%2B6x%29%2Fxy
Next the denominator
%281%2Fx%5E2%29-%2836%2Fy%5E2%29 multiply each term by x%5E2y%5E2%2Fx%5E2y%5E2 and we get
%28y%5E2-36x%5E2%29%2Fx%5E2y%5E2 and we can further simplify this:
%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2 now we can put the numerator and denominator back together
%28%28y%2B6x%29%2Fxy%29%2F%28%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2%29 We will now multiply the numerator and denominator by x%5E2y%5E2%2F%28%28y-6x%29%28y%2B6x%29%29. By doing this, our denominator will become 1.
Now when we start simplifying this expression we end up with:
%28xy%2F%28y-6x%29%29%2F1 and this equals:
xy%2F%28y-6x%29-------------------ans

Hope this helps----ptaylor