SOLUTION: x/(x^2-100)+7/x in factored form pleaseeeee show work

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Question 643999: x/(x^2-100)+7/x in factored form pleaseeeee show work
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%5E2-100%29 + 7%2Fx

Factor x²-100 as (x-10)(x+10)

x%2F%28%28x-10%29%28x%2B10%29%29 + 7%2Fx

The LCD is x(x-10)(x+10)

Multiply the first fraction by x%2Fx since that is the only
factor of the LCD which the first fraction's denominator does not contain.

Multiply the first fraction by %28%28x-10%29%28x%2B10%29%29%2F%28%28x-10%29%28x%2B10%29%29 since they are the factors 
of the LCD which the second fraction's denominator does not contain.

x%2Fx·x%2F%28%28x-10%29%28x%2B10%29%29 + %28%28x-10%29%28x%2B10%29%29%2F%28%28x-10%29%28x%2B10%29%29·7%2Fx

x%5E2%2F%28x%28x-10%29%28x%2B10%29%29 + %287%28x-10%29%28x%2B10%29%29%2F%28x%28x-10%29%28x%2B10%29%29

Multiply out the right numerator (not the denominator)

x%5E2%2F%28x%28x-10%29%28x%2B10%29%29 + %287%28x%5E2-100%29%29%2F%28x%28x-10%29%28x%2B10%29%29

x%5E2%2F%28x%28x-10%29%28x%2B10%29%29 + %287x%5E2-700%29%29%2F%28x%28x-10%29%28x%2B10%29%29

Combine both numerators over the LCD:

%28x%5E2%2B7x%5E2-700%29%2F%28%28x-10%29%28x%2B10%29%29

%288x%5E2-700%29%2F%28x%28x-10%29%28x%2B10%29%29

Since you want everything factored completely,
 factor out 4 in the top:

%284%282x%5E2-175%29%29%2F%28x%28x-10%29%28x%2B10%29%29

Edwin