question about MIT calc 1 implicit diff video

Question

The implicit solution to $y^4+xy^2-2=0$

is written on the board as $$ y^{\prime} = \frac{-y^2}{4y^3+2xy}$$

did I miss something, but can't you factor out a y?

so it should be $$y^{\prime} = \frac{-y}{4y^2+2x}$$

Answer 1

Yes. Given $$y^4+xy^2-2=0,$$ $$y^{\prime} = \frac{-y^2}{4y^3+2xy} = \frac {-y}{4y^2 + 2x}$$

The step written on the blackboard was likely there for pedagogical reasons. I can't explain, however, why it was not then simplified.