Increasing the Reciprocal

Algebra Level 2

In a certain positive fraction \( \frac{a}{b} \), the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by \( 1 \frac{1}{15} \). Find \( a + b \).

Details and assumptions

A positive fraction is a fraction that has a positive value. For example, \( \frac {10}{12} \) and \( \frac { - 2.3}{-0.3} \) are both positive fractions.

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