if twice a number added to 3 is divided by the number plus 1, the result is 3 halves

Answer 1

(2x+3)/(x +1) = 3/2 cross multiply

4x+6 = 3x+3

x=-3

UNLESS you really meant [(2x+3)/x] + 1 =3/2

which is what PEMDAS, order of operations would require, as D, division comes before A addition.

then

(2x+3)/x = 3/2-1 = 1/2

x= 4x+6

3x =-6

x =-2

I'd go with -2. But depending on how you copied the problem it could be either -2 or -3.