\[1)\ \frac{2y + 1}{y^{2} + 6y + 9} - \frac{y - 2}{y^{2} + 3y} =\]
\[= \frac{2y + 1^{\backslash y}}{(y + 3)^{2}} - \frac{y - 2^{\backslash y + 3}}{y(y + 3)} =\]
\[= \frac{2y^{2} + y - \left( y^{2} - 2y + 3y - 6 \right)}{y(y + 3)^{2}} =\]
\[= \frac{2y^{2} + y - y^{2} - y + 6}{y(y + 3)^{2}} =\]
\[= \frac{y^{2} + 6}{y(y + 3)^{2}};\]
\[2)\ \frac{y^{2} + 6}{y(y + 3)^{2}}\ :\frac{y^{2} + 6}{y^{3} - 9y} =\]
\[= \frac{y^{2} + 6}{y(y + 3)^{2}} \cdot \frac{y^{3} - 9y}{y^{2} + 6} =\]
\[= \frac{y\left( y^{2} - 9 \right)}{y(y + 3)^{2}} = \frac{(y - 3)(y + 3)}{(y + 3)^{2}} =\]
\[= \frac{y - 3}{y + 3}.\]
\[Что\ и\ требовалось\ доказать.\]