\(15\dfrac{17}{14}-\left(2\dfrac{3}{19}-9\dfrac{7}{41}\right)=15\dfrac{17}{14}+2\dfrac{3}{19}+9\dfrac{7}{41}=\dfrac{12636}{779}\)
\(15\dfrac{7}{14}-\left(2\dfrac{3}{9}-9\dfrac{7}{41}\right)\)
\(=15\dfrac{7}{14}-\left(2-9+\dfrac{3}{9}-\dfrac{7}{41}\right)\)
\(=15\dfrac{7}{14}-\left(-7+\dfrac{20}{123}\right)\)
\(=15\dfrac{7}{14}-\left(-6\dfrac{103}{123}\right)\)
\(=15\dfrac{7}{14}+6\dfrac{103}{123}\)
\(=21+1\dfrac{83}{246}\)
\(=22\dfrac{83}{246}\)