Question

The sum of a fraction and $3$ times its reciprocal is $\frac{19}{4}$.What is the fraction?

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{5}{4}$
• D. $\frac{4}{5}$

Answer 1

The correct option is A $\frac{3}{4}$

Let the required fraction be $x$.

Then, $x+3\frac{1}{x}=\frac{19}{4}$

$x+\frac{3}{x}=\frac{19}{4}$

$4x^2-19x+12=0$

$(4x-3)(x-4)=0$

$x=\frac{3}{4}$ or $x=4$

Thus, the required fraction is $\frac{3}{4}$.

Hence, option A is correct.