Question Number 173383 by AgniMath last updated on 10/Jul/22
Answered by som(math1967) last updated on 10/Jul/22
$$\frac{\mathrm{1}}{\mathrm{1}+{a}+\frac{\mathrm{2}}{{b}}}\:+\frac{{ac}}{{ac}+\frac{{abc}}{\mathrm{2}}+{ac}.{c}^{−\mathrm{1}} } \\ $$$$\:\:+\frac{{a}}{{a}+{a}.{a}^{−\mathrm{1}} +{ac}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+{a}+{ac}}\:+\frac{{ac}}{{ac}+\mathrm{1}+{a}}\:+\frac{{a}}{{a}+\mathrm{1}+{ac}}\:\bigstar \\ $$$$=\frac{\mathrm{1}+{a}+{ac}}{\mathrm{1}+{a}+{ac}}=\mathrm{1} \\ $$$$\bigstar\:{abc}=\mathrm{2}\Rightarrow\boldsymbol{{ac}}=\frac{\mathrm{2}}{\boldsymbol{{b}}},\:\frac{\boldsymbol{{abc}}}{\mathrm{2}}=\mathrm{1} \\ $$