AMC10 2005 A

AMC10 2005 A · Q2

AMC10 2005 A · Q2. It mainly tests Manipulating equations.

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 $((1 \star 2) \star 3)$?

对于每对实数 $a \neq b$，定义操作 $\star$ 为 $(a \star b) = \frac{a+b}{a-b}$。求 $((1 \star 2) \star 3)$ 的值。

(A) $-\frac{2}{3}$ $-\frac{2}{3}$

(B) $-\frac{1}{5}$ $-\frac{1}{5}$

(D) $\frac{1}{2}$ $\frac{1}{2}$

(E) This value is not defined. 此值未定义。

Answer

Correct choice: (C)

正确答案：（C）

Solution

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

2. (C) 首先有 $(1 \star 2)=\dfrac{1+2}{1-2}=-3.$ 然后 $((1 \star 2)\star 3)=(-3 \star 3)=\dfrac{-3+3}{-3-3}=\dfrac{0}{-6}=0.$

Topics

AL.016 Manipulating equations