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jmc

algebra intermediate

Problem

If

f (x) = \frac{3 x - 2}{x - 2}

, what is the value of

f (- 2) + f (- 1) + f (0)

? Express your answer as a common fraction.

Solution

f (- 2) + f (- 1) + f (0) = \frac{3 ( - 2 ) - 2}{- 2 - 2} + \frac{3 ( - 1 ) - 2}{- 1 - 2} + \frac{3 ( 0 ) - 2}{0 - 2} = \frac{- 8}{- 4} + \frac{- 5}{- 3} + \frac{- 2}{- 2} = 2 + \frac{5}{3} + 1 = \frac{14}{3}

Final answer

\frac{14}{3}