\(A=\frac{1}{x+3}:\left(\frac{x-2}{\left(x+3\right)}+\frac{x+3}{x-2}+\frac{11x+8}{\left(x+3\right)\left(x-2\right)}\right)\)
\(A=\frac{1}{x+3}:\left(\frac{x^2-4x+4+x^2+6x+9+11x+8}{\left(x+3\right)\left(x-2\right)}\right)=\frac{1}{x+3}:\frac{2x^2+13x+21}{\left(x+3\right)\left(x-2\right)}=\frac{x-2}{2x^2+13x+21}\)