To find a rational number x between two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d},\) we use

\(\text{x}=\frac{1}{2}(\frac{a}{b}+\frac{c}{d})\)

Therefore, 

to find rational number x (let) between \(\frac{2}{3}\) and \(\frac{3}{4}\)

\(\text{x}=\frac{1}{2}(\frac{2}{3}+\frac{3}{4})\)

\(\Rightarrow\) \(\text{x}=\frac{1}{2}(\frac{8+9}{12})\)

\(\Rightarrow\) \(\text{x}=\frac{1}{2}\times\frac{17}{12}\)

\(\Rightarrow\) \(\text{x}=\frac{17}{24}\)

Now if we find a rational number between \(\frac{2}{3}\) and \(\frac{17}{24}\) it will also be between \(\frac{2}{3}\) and \(\frac{3}{4}\)since \(\frac{17}{24}\) lies between \(\frac{2}{3}\) and \(\frac{3}{4}\) 

Therefore, 

to find rational number y (let) between \(\frac{2}{3}\)  and \(\frac{17}{24}\)

\(\text{y}=\frac{1}{2}(\frac{2}{3}+\frac{17}{24})\)

\(\Rightarrow\) \(\text{y}=\frac{1}{2}(\frac{16+17}{24})\)

\(\Rightarrow\) \(\text{y}=\frac{1}{2}\times\frac{33}{24}\)

\(\Rightarrow\) \(\text{y}=\frac{33}{48}\)

Now if we find a rational number between \(\frac{17}{24}\) and \(\frac{3}{4}\) it will also be between \(\frac{2}{3}\) and \(\frac{3}{4}\)since \(\frac{17}{24}\) lies between \(\frac{2}{3}\) and \(\frac{3}{4}\) 

Therefore, 

to find rational number z (let) between \(\frac{17}{24}\) and \(\frac{3}{4}\)

\(\text{z}=\frac{1}{2}(\frac{17}{24}+\frac{3}{4})\)

\(\Rightarrow\) \(\text{z}=\frac{1}{2}(\frac{17+18}{24})\)

\(\Rightarrow\) \(\text{x}=\frac{1}{2}\times\frac{35}{24}\)

\(\Rightarrow\) \(\text{z}=\frac{35}{48}\)