I think that this is going to be one of those "duh" questions, but I'm hung up.

I need to convert 8x^2 + 3y^2 = 12 into the standard form of an ellipse. Dividing by 12, I get (2/3)*(x^2) + (y^2)/4 = 1. How do I handle that 2/3 coefficient? Can I factor it to get 2[(x^2)/3 + (y^2)/8] = 1? When I tried this, I don't get the correct vertices or foci, so I don't think this is the right approach. Can anyone help?

Thanks!