Find the values of k for which has one stationary value.

I attempted to differentiate the equation using the cover-up and quotient rule, but the further i go the longer and more messy the result becomes, it'll take too long to post all my workings here

First:

when x=k with (x-k) covered,

then comparing coefficients

Then i inserted these values into the equation the tried to differentiate it with the quotient rule. This is where i get stuck.

thanks