I've tried to simplify this a million different ways, but I can't seem to get the right answer. Please help.
((1/(x+h)^3)-(1/x^3))/8h
Well, try 1,000,001 times.
((1/(x+h)^3)-(1/x^3))/8h
= [ (x^3 - (x+h)^3)/(x^3(x+h)^3) ]/(8h)
= [ ( x^3 - x^3 - 3x^2h - 3xh^2 - h^3)/(x^3(x+h)^3]/)8h)
= [ (-3x^2 h - 3xh^2 - h^3)/(x^3(x-h)^3 ]/(8h)
divide top and bottom by h
= [-3x^2 - 3xh - h^2)/(x^3(x-h)]/8
usually this is a limit question, where h ---> 0
in that case this would reduce to
[-3x^2/x^4]/8
= (-3/8)/x^2