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imc

prealgebra junior

Problem

For each pair of real numbers

a \neq = b

, define the operation

⋆

as

(a ⋆ b) = \frac{a + b}{a - b}

. What is the value of

((1 ⋆ 2) ⋆ 3)

?

(A)

- \frac{2}{3}

(B)

- \frac{1}{5}

(C)

0

(D)

\frac{1}{2}

Solution

((1 ⋆ 2) ⋆ 3) = ((\frac{1 + 2}{1 - 2}) ⋆ 3) = (- 3 ⋆ 3) = \frac{- 3 + 3}{- 3 - 3} = 0 ⟹ 0

Final answer

C