say we have the string $[4;3,2,2]$ and [3;1,1]. they represents $73/17$ and $7/2$. the product of these numbers is $511/34$, which is $[15;34]$ in continued fraction abbreviated notation form.
is there a method or algorithm to compute $[4;3,2,2]*[3;1,1]=[15;34]$? is it possible to do addition, multiplication, division, subtraction with numbers notated like this without converting them to familiar fractions first?