PreCalculus
posted by rocky on .
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(xh)^3 ]/(8h)
divide top and bottom by h
= [3x^2  3xh  h^2)/(x^3(xh)]/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