Question

Please help

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

Answer 1

It is 1-n/n+4.

Answer 2

`(n^2+3n+2)/(n^2+6n+8)-(2n)/(n+4)\\\\=(n^2+2n+n+2)/(n^2+4n+2n+8)-(2n)/(n+4)\\\\=(n(n+2)+1(n+2))/(n(n+4)+2(n+4))-(2n)/(n+4)\\\\=((n+2)(n+1))/((n+2)(n+4))-(2n)/(n+4)\\\\=(n+1)/(n+4)-(2n)/(n+4)=(n+1-2n)/(n+4)=(1-n)/(n+4)`


`Answer:\ \boxed{B.\ (1-n)/(n+4)}`