Simplifiable

Let us take two fractions \(\dfrac{a}{b}\) and \(\dfrac{c}{d}\), where \(a,b,c\) and \(d\) are pairwise coprime positive integers.

When is \(\dfrac{ad+cb}{bd}\) simplifiable? That is, when the numerator and denominator are divisible by the same number? Find the number of all such quadruplets \((a,b,c,d)\) where \(a,b,c,d<16\).

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