Increasing the Reciprocal

Algebra Level 2

In a certain positive fraction ab \frac{a}{b} , the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1115 1 \frac{1}{15} . Find a+b a + b .

Details and assumptions

A positive fraction is a fraction that has a positive value. For example, 1012 \frac {10}{12} and 2.30.3 \frac { - 2.3}{-0.3} are both positive fractions.

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