Question

The sum of a fraction and its reciprocal is $1\frac{1}{2}$ more than the fraction. Find the fraction.

Answer 1

Let the fraction be $\frac{x}{y}$.

According to the question,

$\frac{x}{y}+\frac{y}{x}=\frac{x}{y}+1\frac{1}{2}$

$\frac{x}{y}+\frac{y}{x}=\frac{x}{y}+\frac{3}{2}$

$\frac{y}{x}=\frac{3}{2}$

$\frac{x}{y}=\frac{2}{3}$

Hence, the fraction is $\frac{2}{3}$.