Question

$\frac{5p-6q}{3p+4q}$

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \frac{p}{q}=\frac{6}{5} \\ \mathrm{On}\mathrm{dividing}\mathrm{each}\mathrm{term}\mathrm{by}q\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{expression},\mathrm{we}\mathrm{get}: \\ \frac{5p-6q}{3p+4q}=\frac{5\left({\displaystyle \frac{p}{q}}\right)-6\left({\displaystyle \frac{q}{q}}\right)}{3\left({\displaystyle \frac{p}{q}}\right)+4\left({\displaystyle \frac{q}{q}}\right)} \\ =\frac{5\left({\displaystyle \frac{p}{q}}\right)-6}{3\left({\displaystyle \frac{p}{q}}\right)+4} \\ \mathrm{Also},\mathrm{we}\mathrm{know}\mathrm{that}\frac{p}{q}=\frac{6}{5}. \\ \therefore \frac{5p-6q}{3p+4q}=\frac{5\times {\displaystyle \frac{6}{5}}-6}{3\times {\displaystyle \frac{6}{5}}+4} \\ =\frac{0}{{\displaystyle \frac{38}{5}}} \\ =0 \end{gathered}$$