SOLUTION: Simplify the difference n^2 - 10n + 24/n^2 - 13n + 42 - 9/n - 7

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Question 626015: Simplify the difference
n^2 - 10n + 24/n^2 - 13n + 42 - 9/n - 7
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
%28n%5E2+-+10n+%2B+24%29%2F%28n%5E2+-+13n+%2B+42%29  -  9%5E%22%22%2F%28n%5E%22%22+-+7%29

Factor the numerator and denominator of the first fraction:

%28%28n-6%29%28n-4%29%29%2F%28%28n-7%29%28n-6%29%29  -  9%2F%28n+-+7%29

Cancel the (n-6)'s in the first fraction:

%28%28cross%28n-6%29%29%28n-4%29%29%2F%28%28n-7%29%28cross%28n-6%29%29%29  -  9%2F%28n+-+7%29

%28n-4%29%2F%28n+-+7%29 - 9%2F%28n+-+7%29

Wow! We didn't even need to get the LCD because it already has the LCD.
We combine the two numerators over the LCD:

%28n-4-9%29%2F%28n+-+7%29

%28n-13%29%2F%28n+-+7%29

Edwin