Question Number 173339 by AgniMath last updated on 10/Jul/22
Commented by som(math1967) last updated on 10/Jul/22
$$\:{if}\:{it}\:\frac{{x}}{{a}+{x}}\:+\frac{{y}}{{b}+{y}}\:+\frac{{z}}{{c}+{z}} \\ $$$$=\frac{{ax}}{{a}^{\mathrm{2}} +{ax}}\:+\frac{{by}}{{b}^{\mathrm{2}} +{by}}\:+\frac{{cz}}{{c}^{\mathrm{2}} +{cz}} \\ $$$$=\frac{{ax}}{{by}+{cz}+{ax}}\:+\frac{{by}}{{ax}+{cz}+{by}}+\frac{{cz}}{{ax}+{by}+{cz}} \\ $$$$=\frac{{ax}+{by}+{cz}}{{ax}+{by}+{cz}}=\mathrm{1} \\ $$