Question

6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction, if both fractions are positive and real?

• A. $\frac{5}{7}$
• B. $\frac{7}{3}$
• C. $\frac{6}{7}$
• D. B or C
• E. None of the above

Answer 1

The correct option is B $\frac{7}{3}$

Let the fraction be = x

Then, 6x - $\frac{7}{x}$ = 11 $\Rightarrow$ 6x${}^2$ - 7 = 11x

6x${}^2$ - 11x - 7 = 0

$\text{x}=\frac{11\pm 17}{12}=\frac{7}{3}\text{or}\frac{-1}{2}$