\[\frac{y^{2} + 6y - 1}{y + 6} =\]
\[= \frac{y^{2} + 6y}{y + 6} - \frac{1}{y + 6} =\]
\[= \frac{y(y + 6)}{y + 6} - \frac{1}{y + 6} = y - \frac{1}{y + 6}\]