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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