To find the difference in simplest form, we need to find a common denominator for the two fractions.
First, factor the denominators:
n^2 + 3n + 2 = (n + 1)(n + 2)
n^2 + 6n + 8 = (n + 2)(n + 4)
The common denominator will be (n + 2)(n + 4).
Rewrite the expression with the common denominator:
(n^2 + 3n + 2)/(n^2 + 6n + 8) - (2n)/(n + 4) = ((n + 1)(n + 2))/(n + 4)(n + 2) - (2n(n + 2))/(n + 4)(n + 2)
Now, combine the fractions:
((n + 1)(n + 2) - 2n(n + 2))/(n + 4)(n + 2)
(n^2 + 3n + 2 - 2n^2 - 4n)/(n + 4)(n + 2)
(n^2 + 3n + 2 - 2n^2 - 4n)/(n + 4)(n + 2)
(-n^2 - n + 2)/(n + 4)(n + 2)
(n^2 + n - 2)/(n + 4)(n + 2)
(n + 2)(n - 1)/(n + 4)(n + 2)
Therefore, the difference in simplest form is (n - 1)/(n + 4). This corresponds to answer choice B: 1 - n/n+4.
what is the difference in simplest form? (n^2+3n+2/n^2+6n+8)-(2n/n+4)
A. 1/n+2
B. 1-n/n+4
C. 3n+1/n+4
D. n^2+2+2/n^2+6n+8
1 answer