looks ok to me ...
I'm not sure about the result.
f(x)= (x^{3}+x^{2})/(x^{2}-4)
=(x^{2}-4)(3x^{2}+2x) - (x^{3}+x^{2})(2x) / (x^{2}-4)^{2 }
=(3x^{4}+2x^{3}-12x^{2}-8x) - (2x^{4} + 2x^{3}) / (x^{2}-4)^{2 }
=(x^{4}-12x^{2}-8x) / (x^{2}-4)^{2 Would this be the simplified first derivative?}
Thanks. Now for finding a possible critical value for increasing and decreasing intervals, I would take the numerator = 0. I'm having trouble on how I should go about that. I've looked up information on how to do critical values, but each has you factoring it down into (x-1) type terms. Meanwhile I have, x^{4}-12x^{2}-8x = 0. I can't factor out anything more than x.