Solve for y in terms of x. x=(y+2)/(y+3)

Multiply both sides by y+3 to get xy+3x=y+2. Subtract 2 from both sides as well as xy, getting 3x-2=y-xy. After that, divide y from both sides to get (3x-2)/y=1-x. After that, divide both sides by (3x-2) to get 1/y=(1-x)/(3x-2). After that, multiply both sides by y to get 1=y(1-x)/(3x-2), and then multiply both sides by
(3x-2)/(1-x) to get  (3x-2)/(1-x)=y