A positive number exceeds its reciprocal by $\frac{15}{4}$. What is the number?

Explanation

1. 01

   $x - \frac{1}{x} = \frac{15}{4}$; multiply by $4x$: $4x^2 - 15x - 4 = 0$.

2. 02

   $(4x + 1)(x - 4) = 0$, so $x = 4$ or $x = -\frac{1}{4}$.

3. 03

   The number is positive, so $x = 4$. Check: $4 - \frac{1}{4} = \frac{15}{4}$.