Pre-Calculus

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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

  • Pre-Calculus -

    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

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