If a>0 and b>0, a new operation \(\nabla\) is defined as follows:\(a \nabla b = \dfrac{a + b}{1 + ab}.\)For example,\(3 \nabla 6 = \dfrac{3 + 6}{1 + 3 \times 6} = \dfrac{9}{19}.\)For some values of x and y, the value of \(x \nabla y\) is equal to \(\dfrac{x + y}{17}\). How many possible ordered pairs of positive integers $x$ and $y$ are there for which this is true?
Don't quite understand your question! Do you mean that for some values of a, b and for some values of x, y:
(a + b) / (1 + a*b) = (x + y) / 17 ????.
