What is the difference in simplest form?
(n^2 + 3n + 2)/(n^2 + 6n + 8) - 2n/n+4
1/n + 2
1-n/n+4
3n+1/n+4
n^2 + 2 + 2/n^2 + 6n + 8
The expression is:
(n^2 + 3n + 2)/(n^2 + 6n + 8) - 2n/(n+4)
First, factor the denominators:
(n^2 + 3n + 2) = (n + 2)(n + 1)
(n^2 + 6n + 8) = (n + 2)(n + 4)
Now rewrite the expression:
[(n + 2)(n + 1)] / [(n + 2)(n + 4)] - 2n/(n+4)
Next, simplify:
(n+1)/(n+4) - 2n/(n+4)
Now that both fractions have a common denominator, we can combine them:
[(n + 1) - 2n] / (n + 4)
n + 1 - 2n / (n + 4)
Now simplify:
(1 - n) / (n + 4)
Therefore, the difference in simplest form is: 1 - n / (n + 4) or 1 - n/n + 4