Question

What should be added to $\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\right)$ to get 3?

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{added}. \\ \therefore x+(\frac{1}{2}+\frac{1}{3}+\frac{1}{5})=3 \\ \Rightarrow x+(\frac{15}{30}+\frac{10}{30}+\frac{6}{30})=3 \\ \Rightarrow x+\left(\frac{15+10+6}{30}\right)=3 \\ \Rightarrow x+\frac{31}{30}=3 \\ \Rightarrow x=\frac{3}{1}-\frac{31}{30} \\ \Rightarrow x=\frac{90}{30}-\frac{31}{30} \\ \Rightarrow x=\frac{90-31}{30} \\ \Rightarrow x=\frac{59}{30} \end{gathered}$$