AMC12 2017 B

AMC12 2017 B · Q3

AMC12 2017 B · Q3. It mainly tests Manipulating equations.

Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{3x + y}{x - 3y} = -2$. What is the value of $\frac{x + 3y}{3x - y}$?

假设 $x$ 和 $y$ 是非零实数，使得 $\frac{3x + y}{x - 3y} = -2$。求 $\frac{x + 3y}{3x - y}$ 的值？

(A) -3 -3

(B) -1 -1

(D) 2 2

(E) 3 3

Answer

Correct choice: (D)

正确答案：（D）

Solution

The given equation implies that $3x+y = -2(x-3y)$, which is equivalent to $x = y$. Therefore $\frac{x + 3y}{3x - y} = \frac{4y}{2y} = 2$.

给定方程意味着 $3x+y = -2(x-3y)$，这等价于 $x = y$。因此 $\frac{x + 3y}{3x - y} = \frac{4y}{2y} = 2$。

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