Simplify the difference quotient

[f(x) − f(a]/[x − a]

if x ≠ a.
f(x) = SQROOT of (x − 27)
(Hint: Rationalize the numerator.)

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asked by AR.
  1. y(x) = (x-27)^.5

    y(a) = (a -27)^.5

    y(x) -y(a) = (x-27)^.5 - (a-27)^.5)
    then multiply top and bottom by
    (x-27)^.5 + (a-27)^.5)
    and get
    (x-27)-(a-27)/{(x-a)[(x-27)^.5 - (a-27)^.5)]}

    = (x-a)/{(x-a)[(x-27)^.5 - (a-27)^.5)]}

    = 1/[(x-27)^.5 - (a-27)^.5)]

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    posted by Damon

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