Math CentralQuandaries & Queries


Question from Rita, a student:

Find the difference quotient of f, that is, find [f (x + h) - f (x)]/h, where
h does not = 0 for the given function. Be sure to simplify.

f(x) = 1/(x + 3)

Hi Rita,

After substitution this is how your difference function of f looks:

difference quotient

Multiply the numerator and denominator of the right side by the greatest common denominator of 1/(x+3) and 1/(x+h+3) to greatly simplify the question. The answer is much more apparent after you get rid of the fractions in the numerator.

Hope this helps,

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