\(\frac{3}{2x+6}+\frac{x-2}{x^2+6x+9}\)
\(=\frac{3}{2\left(x+3\right)}+\frac{x^2}{\left(x+3\right)^2}\)
\(=\frac{3\left(x+3\right)}{2\left(x+3\right)\left(x+3\right)}+\frac{2x^2}{2\left(x+3\right)\left(x+3\right)}\)
\(=\frac{2x^2+3x+9}{2\left(x+3\right)^2}\)