Ta có mẫu số là
$\dfrac{3}{13.15} + \dfrac{3}{14.16} + \dfrac{3}{15.17} = \dfrac{3}{2} \left(\dfrac{2}{13.15} + \dfrac{2}{14.16} + \dfrac{2}{15.17} \right)$
$= \dfrac{3}{2} \left( \dfrac{1}{13} - \dfrac{1}{15} + \dfrac{1}{14} - \dfrac{1}{16} + \dfrac{1}{15} - \dfrac{1}{17} \right)$
$= \dfrac{3}{2} \left( \dfrac{1}{13} - \dfrac{1}{16} + \dfrac{1}{14} - \dfrac{1}{17} \right)$
$= \dfrac{3}{2} \left( \dfrac{3}{13.16} + \dfrac{3}{14.17} \right)$
$= \dfrac{9}{2} \left( \dfrac{1}{13.16} + \dfrac{1}{14.17} \right)$
Mặt khác, tử số là
$\dfrac{2}{13.16} + \dfrac{2}{14.17} = 2 \left( \dfrac{1}{13.16} + \dfrac{1}{14.17} \right)$
Khi đó, ta có
$\dfrac{\frac{2}{13.16} + \frac{2}{14.17}}{\frac{3}{13.15} + \frac{3}{14.16} + \frac{3}{15.17}} = \dfrac{2 \left( \frac{1}{13.16} + \frac{1}{14.17} \right)}{\frac{9}{2} \left( \frac{1}{13.16} + \frac{1}{14.17} \right)} = \dfrac{2}{\frac{9}{2}} = 9$
