б) \frac{x+3}{x^2+9}\cdot (\frac{x+3}{x-3}+ \frac{x-3}{x+3})

б)

$$\frac{x+3}{x^2+9}\cdot (\frac{x+3}{x-3}+ \frac{x-3}{x+3}) = \frac{x+3}{x^2+9} \cdot (\frac{(x+3)^2+(x-3)^2}{(x-3)(x+3)}) = \frac{x+3}{x^2+9} \cdot (\frac{x^2+6x+9+x^2-6x+9}{x^2-9}) = \frac{x+3}{x^2+9} \cdot (\frac{2x^2+18}{x^2-9}) = \frac{(x+3)2(x^2+9)}{(x^2+9)(x^2-9)} = \frac{2(x+3)}{(x-3)(x+3)} = \frac{2}{x-3}$$.

Ответ: $$\frac{2}{x-3}$$