Question

对每对满足 $a \neq b$ 的实数，定义运算 $\star$ 为 $(a \star b) = \frac{a+b}{a-b}.$

求 $((1 \star 2) \star 3)$ 的值。

For each pair of real numbers $a \neq b,$ define the operation $\star$ as $(a \star b) = \frac{a+b}{a-b}.$

What is the value of $((1 \star 2) \star 3)?$

$-\dfrac{2}{3}$

$-\dfrac{1}{5}$

$0$

$\dfrac{1}{2}$

这个值未定义。

This value is not defined.

首先， $(1 \star 2) = \dfrac{1+2}{1-2} = \dfrac{3}{-1} = -3$ 。然后， $(-3 \star 3) = \dfrac{-3+3}{-3-3} = \dfrac{0}{-6} = 0$ 。

所以正确答案是 C。

First $(1 \star 2) = \dfrac{1+2}{1-2} = \dfrac{3}{-1} = -3.$ Then $(-3 \star 3) = \dfrac{-3+3}{-3-3} = \dfrac{0}{-6} = 0.$

Thus, the correct answer is C.