I have a question which I thought was simple enough, but have somehow got lost for quite a while on it. I need to maximise the following equation with respect to the variable x. a and b are constants.

Making use of the quotient rule, I got the partial derivative with respect to x to be:

Now solving for x, I thought, would be the easy part. But I've spent quite a while now just lost in the algebra. Is there any tips or hints with regards to getting the answer out?