$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$
$${\frac{{\mathtt{1}}}{{\mathtt{7}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{8}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}}$$ Hauptnenner = 504
=> $${\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}}$$
$${\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}} = {\frac{{\mathtt{919}}}{{\mathtt{504}}}} = {\mathtt{1.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$
$${\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}} = {\mathtt{30}}$$ ;
$${\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{415}}}{{\mathtt{504}}}} = {\mathtt{31.823\: \!412\: \!698\: \!412\: \!698\: \!4}}$$
Ergebnis: $$31\frac{415}{504}$$
Gruß radix
!