Question

Find three rational numbers between (a-b)^-1 and (a^-1b^-1) given that a=2/3',b=3/4.

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{a}=\frac{2}{3}\mathrm{and}\mathrm{b}=\frac{3}{4} \\ {\left(\mathrm{a}-\mathrm{b}\right)}^{-1}=\frac{1}{\mathrm{a}-\mathrm{b}}=\frac{1}{\frac{2}{3}-\frac{3}{4}}=\frac{12}{8-9}=-12 \\ \mathrm{and} \\ {\mathrm{a}}^{-1}{\mathrm{b}}^{-1}=\frac{1}{\mathrm{ab}}=\frac{1}{{\displaystyle \frac{2}{3}}\times {\displaystyle \frac{3}{4}}}=2 \\ \mathrm{Now}\mathrm{three}\mathrm{rational}\mathrm{numbefr}\mathrm{between}-12\mathrm{and}2\mathrm{or}\frac{-24}{2},\frac{4}{2} \\ =\frac{-23}{2},\frac{-22}{2},\frac{-21}{2} \\ \mathrm{Regards} \end{gathered}$$