#5) n^2+3n+2 over n^2+5n+6 minus 2n over n+3
step one: factor n^2 + 3n+2
(n+1)(n+2) over n^2+5n+6 minus 2n over n+3
step two: factor n^2+5n+6
(n+1)(n+2) over (n+2)(n+3) minus 2n over n+3
step three: cancel n+2
n+1 over n+3 minus 2n over n+3
step four: join the denominators
n+1-2n over n+3
step five: collect like terms
(n-2n)+1 over n+3
step six: simplify (n-2n)+1 to -n+1
-n+1 over n+3
step seven: regroup terms
1-n over n+3
