SOLUTION: What is the difference in simplest form? n^2+3n+2/n^2+6b+8 - 2n/n+4

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Question 706951: What is the difference in simplest form?
n^2+3n+2/n^2+6b+8 - 2n/n+4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In the future, please put parentheses around multiple-term numerators and denominators. Without the parentheses it is difficult for us to determine what is in a numerator or denominator and what is in separate terms. What you posted meant:
n%5E2%2B3n%2B2%2Fn%5E2%2B6b%2B8+-+2n%2Fn%2B4
which is probably not what you meant. Clearly expressed problems are more like to get quick responses.

I'm guessing you meant:
%28n%5E2%2B3n%2B2%29%2F%28n%5E2%2B6b%2B8%29+-+2n%2F%28n%2B4%29
If this is correct then keep reading. If not then re-post your question using parentheses to make it clear.

First let's factor the numerators and denominators. This will help us:
  • find the lowest common denominator; and
  • possibly reduce some fractions
The numerator and denominator in the first fraction will each factor:
%28%28n%2B2%29%28n%2B1%29%29%2F%28%28n%2B2%29%28x%2B4%29%29+-+2n%2F%28n%2B4%29
As we can see, there is a factor we can cancel in the first fraction:

leaving:
%28n%2B1%29%2F%28x%2B4%29+-+2n%2F%28n%2B4%29
Not only did the first fraction reduce but we got common denominators at the same time! So we can proceed with the subtraction:
%28%28n%2B1%29+-+%282n%29%29%2F%28n%2B4%29
which simplifies to:
%28-n%2B1%29%2F%28n%2B4%29