try this one !!

(3x^2) / ((y^2)+1) + y = 3x + 1

3x^2((y^2)+1)^-1 + y = 3x + 1

6x((y^2)+1)^-1 - 3x^2((y^2)+1)^-2(2ydy/dx) + dy/dx = 3

6x((y^2)+1)^-1 - 6x^2(ydy/dx)((y^2)+1)^-2 + dy/dx = 3

6x((y^2)+1)^-1 - (6yx^2((y^2)+1)^-2 + 1)dy/dx = 3

6x((y^2)+1)^-1 - 3 = (6yx^2((y^2)+1)^-2 + 1)dy/dx

(6x / ((y^2) + 1) - 3) / ((6yx^2/((y^2)+1)^2) + 1) = dy/dx

it's been re-corrected. dy/dx didn't have the '3' factor to factor out.