Math plz ! show work giving brainlist

#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