The sum of a fraction and 3 times its reciprocal is 19/4. What is the fraction?
Let that fraction be $$\frac{1}{x}$$
$$ \frac{1}{x} + 3x = \frac{19}{4}$$
$$\Rightarrow (1+3x^{2}) = \frac{19}{4} \times x$$
$$\Rightarrow 12x^{2}-19x+4 = 0$$
$$\Rightarrow(x-\frac{16}{12})(x-\frac{3}{12})=0$$
$$\Rightarrow(x-\frac{4}{3})(x-\frac{1}{4})=0$$
$$\Rightarrow x = 4/3 or 1/4$$
$$\Rightarrow \text{fraction} = \frac{1}{x} = 3/4 \text(or) 4$$
so the answer is option A.
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