core 3 differentiation

For each of the following curves, find dy/dx and determine the exact x-coordinate of the stationary point:
y= x^2/lnx

i know that to differentiate this, i need to use the quotient rule:
dy/dx = (lnx2x - x^2*1/x)/ (lnx)^2
i made dy/dx equal to zero but i'm not sure how to solve this after that?

You have numerator = 0 so then just factor out the x

if i factor out x, i got:
x(ln2 - x*1/x) / (lnx)^2

the mark scheme says if i solve this, i must get x=e^1/2. how do i get this?

Set it =0 then it’s obvious!

I genuinely cant see it? could you elaborate please?