My course

You are correct, we have a violation of algebra.

$dy/dx=\frac{1}{\left(\frac{3}{2\sqrt{y}}+1\right)}$ =$\frac{2\sqrt{y}}{3+2\sqrt{y}}$

shouldn't -4x^4 + 6x^4 equal 2x^4 and not -2x^4?

How come could we just add dy/dx to 3/2squareroot(y) times dy/dx in this question? Is this a mistake? The answer I got was y'=1 / 3/squareroot(y) +1 (before simplifying any further.