№6.* Упростите выражение 2y y+3 +(y-3)2. ( 2 9-6y+y2 + 1 9-y2 )

Упростим выражение $$\frac{2y}{y+3} + (y-3)^2 \cdot (\frac{2}{9-6y+y^2} + \frac{1}{9-y^2})$$.

$$\frac{2y}{y+3} + (y-3)^2 \cdot (\frac{2}{9-6y+y^2} + \frac{1}{9-y^2}) = \frac{2y}{y+3} + (y-3)^2 \cdot (\frac{2}{(y-3)^2} + \frac{1}{(3-y)(3+y)}) = \frac{2y}{y+3} + (y-3)^2 \cdot (\frac{2}{(y-3)^2} - \frac{1}{(y-3)(y+3)}) = \frac{2y}{y+3} + (2 - \frac{(y-3)^2}{(y-3)(y+3)}) = \frac{2y}{y+3} + (2 - \frac{y-3}{y+3}) = \frac{2y + 2(y+3) - (y-3)}{y+3} = \frac{2y + 2y+6 - y+3}{y+3} = \frac{3y+9}{y+3} = \frac{3(y+3)}{y+3} = 3$$

Ответ: 3