${(\frac{x+5}{x^2+5x+6}+\frac{2}{x+3}-\frac{2}{x+2})}^2:\frac{x-1}{x^3+3x^2-4}=$

$={(\frac{x+5}{\left(x+3\right)\left(x+2\right)}+\frac{2}{x+3}-\frac{2}{x+2})}^2:\frac{x-1}{{\left(x+2\right)}^2\left(x-1\right)}=$

$={\left(\frac{x+5+2\left(x+2\right)-2\left(x+3\right)}{\left(x+3\right)\left(x+2\right)}\right)}^2:\frac{1}{{\left(x+2\right)}^2}=$

$={\left(\frac{x+5+2x+4-2x-6}{\left(x+3\right)\left(x+2\right)}\right)}^2·{\left(x+2\right)}^2=$

$={\left(\frac{x+3}{\left(x+3\right)\left(x+2\right)}\right)}^2·{\left(x+2\right)}^2=$

$=\frac{1}{{\left(x+2\right)}^2}·{\left(x+2\right)}^2=1$