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 $qs=21k$.

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Numerator:

$7pr-qs=7(5k)-21k$

$=35k-21k$

$=14k$

Denominator:

$6qs-21pr=6(21k)-21(5k)$

$=126k-105k$

$=21k$

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$\dfrac{7pr-qs}{6qs-21pr}=\dfrac{14k}{21k}=\dfrac{2}{3}$