将 $\dfrac{6x^2-9x-16}{2x^2-5x-12}$ 表示为部分分式。

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。

分子分母同次，先除得常数，再分解二次分母并拆成两个简单分式。

Factoring the denominator,

Polynomial division gives

Write the remainder fraction as $B/(2x+3)+C/(x-4)$. Then

Putting $x=-3/2$ gives $11=-11B/2$, so $B=-2$. Putting $x=4$ gives $44=11C$, so $C=4$.

Hence