# 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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