calc

Suppose that f(x) = 1/x. Find a simplified expression for f(x)-f(a)/x-a

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  1. f(x) = 1/x
    so, f(a) = 1/a

    (f(x) - f(a))/(x-a) , notice the necessary placing of brackets
    = (1/x - 1/a)/(x-a)
    = [ (a-x)/(ax) ]/(x-a)
    = (a-x)/(ax) * 1/(x-a)
    = -1/(ax)

    notice (a-x)/(x-a)
    = -(x-a)/(x-a) = -1

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  2. got it, thanks!

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