б) \(\frac{1}{6} \left(\frac{y^2+6y+9}{y^2-9} - \frac{3-y}{5}\right)\)

Решение:

Упростим выражение:

\[ \frac{1}{6} \left(\frac{y^2+6y+9}{y^2-9} - \frac{3-y}{5}\right) \]\[ = \frac{1}{6} \left(\frac{(y+3)^2}{(y-3)(y+3)} - \frac{3-y}{5}\right) \]\[ = \frac{1}{6} \left(\frac{y+3}{y-3} - \frac{3-y}{5}\right) \]\[ = \frac{1}{6} \left(\frac{y+3}{y-3} + \frac{y-3}{5}\right) \]

Найдем общий знаменатель \( 5(y-3) \):

\[ = \frac{1}{6} \left(\frac{5(y+3) + (y-3)(y-3)}{5(y-3)}\right) \]\[ = \frac{1}{6} \left(\frac{5y+15 + y^2 - 6y + 9}{5(y-3)}\right) \]\[ = \frac{1}{6} \left(\frac{y^2 - y + 24}{5(y-3)}\right) \]\[ = \frac{y^2 - y + 24}{30(y-3)} \]

Ответ: \( \frac{y^2 - y + 24}{30(y-3)} \).