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Question-173339




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

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