solution attempt: Book asks one to to try solving two ways once with quotient rule and once simplifying first. I have shown here only the quotient rule solution as that is giving me enough trouble to warrant a post

With quotient rule,

this is where I am reluctant to continue as I'm unsure how to go about simplifying the exponents, in doing so I end up with:

I could eliminate the but I get the distinct feeling I performed an error 2 expressions ago... please show me my error