Mathematics - Sequence & Series Question with Solution | TestHub

$\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{b}}=\frac{1}{\mathrm{b}}-\frac{1}{\mathrm{c}}$ $\therefore \left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}-\frac{1}{\mathrm{c}}\right)\left(\frac{1}{\mathrm{b}}+\frac{1}{\mathrm{c}}-\frac{1}{\mathrm{a}}\right)$ $=\left(\frac{2}{\mathrm{a}}-\frac{1}{\mathrm{b}}\right)\left(\frac{2}{\mathrm{c}}-\frac{1}{\mathrm{b}}\right)=\frac{4}{\mathrm{ac}}-\frac{1}{\mathrm{b}}\left(\frac{2}{\mathrm{a}}+\frac{2}{\mathrm{c}}\right)+\frac{1}{{\mathrm{b}}^2}$ $=\frac{4}{\mathrm{ac}}-\frac{2}{\mathrm{b}}\left(\frac{2}{\mathrm{b}}\right)+\frac{1}{{\mathrm{b}}^2}=\frac{4}{\mathrm{ac}}-\frac{3}{{\mathrm{b}}^2}$