Thread: Help finding derivative using definition (which results in a complex fraction)

Hello! This is the last problem of the night (I promise!). Will someone please help me with the following problem; if I could use the quotient rule I wouldn't have had any problems, but here is the question:

Find the derivative of

using the definition of derivative.
State the domain of the function and the domain of its derivative.

When I worked it out, this was what I got:


But the answer I got using Mathway.com was:


I could DEFINITELY use some help. Where did I go wrong?

so

I can't believe I made so many basic mistakes. Thank you so much for your help!! :-)