一条曲线的方程为 $y=\frac{2x^2+7x}{3x^2-1}$。

求曲线在 $x=1$ 处的法线方程。答案写成 $ax+by+c=0$ 的形式，其中 $a$、$b$ 和 $c$ 为整数。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

用商法则求切线斜率，再取负倒数得到法线斜率。求出曲线上的点后，用点斜式整理。

By the quotient rule,

At $x=1$, $y=9/2$ and the derivative is $(22-54)/4=-8$. The normal therefore has gradient $1/8$, giving

Multiplying by $8$ gives $8y-36=x-1$. Rearranging into the required integer form gives $x-8y+35=0$.