The sum of a fraction and 3 times its reciprocal is 31/6. What is the fraction?
Let that fraction be $$\frac{1}{x}$$
$$ \frac{1}{x} + 3x = \frac{31}{6}$$
$$\Rightarrow (1+3x^{2}) = \frac{31}{6} \times x$$
$$\Rightarrow 18x^{2}-31x+6 = 0$$
$$\Rightarrow(x-\frac{27}{18})(x-\frac{4}{18})=0$$
$$\Rightarrow(x-\frac{3}{2})(x-\frac{2}{9})=0$$
$$\Rightarrow x = 3/2 or 2/9$$
$$\Rightarrow \text{fraction} = \frac{1}{x} = 2/3 \text(or) 9/2$$
so the answer is option B.
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