An easy number theory problem

Number Theory Level pending

Positive integers \(a\), \(b\), \(c\), and \(d\) are such that \(\gcd (a,b)=1\) and \(a<b\), and \(\gcd(c,d)=1\) and \(c<d\). Then \(\dfrac{a}{b}+\dfrac{c}{d}=1\) is true only if \(b=d\).

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