If $\frac{p}{q}=\frac{3}{7}$ and $\frac{r}{s}=\frac{5}{9}$, the value of $\frac{7pr-qs}{6qs-21pr}$ is

Multiply the two given ratios: $\dfrac{pr}{qs}=\dfrac{p}{q}\times\dfrac{r}{s}=\dfrac{3}{7}\times\dfrac{5}{9}=\dfrac{5}{21}$ So take $pr=5k$ and $qs=21k$. Numerator: $7pr-qs=7(5k)-21k$ $=35k-21k$ $=14k$ Denominator: $6qs-21pr=6(21k)-21(5k)$ $=126k-105k$ $=21k$ $\dfrac{7pr-qs}{6qs-21pr}=\dfrac{14k}{21k}=\dfrac{2}{3}$