Math HELP! How do you do this

Problem is 3sin^2x+4sinx+1 divided by sin^2x+2sinx+1 For the answer I got 3 ?

3sin^2x+4sinx+1 can be factored as (3sinx +1)(sinx+1)

sin^2x+2sinx+1 can be factored as (sinx+1)(sinx+1)

So given expression becomes,

(3sinx +1)(sinx+1)/(sinx+1)(sinx+1)

Divide out common factor sinx+1

(3sinx +1)/(sinx+1) =================> Answer :)>

I changed sin(x) to y
If you factor the top and bottom.
Numerator: (y+1)*(3y+1)
Denominator: (y+1)*(y+1)
Which would simplify to (3y+1)/(y+1)==(3sin(x)+1)/(sin(x)+1)
Are you taking the limit of this or just simplifying.