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A curious sequence of rationals: finite or infinite?

Consider the following function repeatedly applied to a rational $r = a/b$ in lowest terms: $f(a/b) = (a b) / (a + b - 1)$. So, $f(2/3) = 6/4 = 3/2$. $f(3/2) = 6/4 = 3/2$. I am wondering if it is ...