The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, the fraction becomes $\frac{4}{5}$. What is the original fraction?

Explanation

1. 01

   Let the denominator be $d$; the numerator is $d - 3$.

2. 02

   $\frac{d - 3 + 2}{d + 2} = \frac{4}{5}$, so $5(d - 1) = 4(d + 2)$.

3. 03

   $5d - 5 = 4d + 8$, so $d = 13$. The fraction is $\frac{10}{13}$.

4. 04

   Check: $\frac{12}{15} = \frac{4}{5}$.