# Fraction Fun

It's obvious to see that $\dfrac{30}{43} = \cfrac1{1 + \cfrac1{2 + \cfrac1{3 + \cfrac14}}} .$ But does there exist another ordered quadruplet of positive integers $$(a,b,c,d)$$ other than $$(1,2,3,4)$$ such that $\dfrac{30}{43} = \cfrac1{a + \cfrac1{b + \cfrac1{c + \cfrac1d}}}?$

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