$$\frac{x^{2}+6x+9}{x^{2}+3x+2}\div\frac{x+3}{x-1}$$
$\frac{\left(x-1\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)}$
$$\frac{\left(x^{2}+6x+9\right)\left(x-1\right)}{\left(x^{2}+3x+2\right)\left(x+3\right)}$$
$$\frac{\left(x-1\right)\left(x+3\right)^{2}}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$
$$\frac{\left(x-1\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)}$$
$$\frac{x^{2}+2x-3}{x^{2}+3x+2}$$
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$\frac{x^{2}+2x-3}{x^{2}+3x+2}$
