Problem using the difference quotient

Hello,

I'm trying to differentiate a sum of functions by means of the difference quotient from a question in my book. The derivative is a given, but I can't end up at the final result (I can, but only if I use )

I feel like I'm close but I now need assistance.

Now this is where I'm stuck. If I assume I can eliminate by way of the difference of two squares. Then I can multiply both the numerator and denominator by in order to replace it with in the numerator.

As for again I think I can eliminate the squares to a more easier form to deal with by way of the difference of two squares but don't know how?

Thank you for your attention.

Re: Problem using the difference quotient

Re: Problem using the difference quotient