I started studying continued fractions..., a vast subject. ( 'new land!' )
Here I calculate the Extended GCD of $9976$ and $6961$ using Blankinship's matrix method. A byproduct of the calculation ( column 1 ) are the numbers for expressing $\frac{9976}{6961}$ as a finite continued fraction.
$\left(
\begin{array}{cccc}
 &  & 9976 & 6961 \\
 & 9976 & 1 & 0 \\
1 & 6961 & 0 & 1 \\
2 & 3015 & 1 & 1 \\
3 & 931 & 2 & 3 \\
4 & 222 & 7 & 10 \\
5 & 43 & 30 & 43 \\
6 & 7 & 157 & 225 \\
7 & 1 & 972 & 1393\\
& 0 & 6961 & 9976 \\
\end{array}
\right)$
$\frac{9976}{6961}=1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\frac{1}{6+\frac{1}{7}}}}}}$
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