remember
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
so
first factor them
\(( \frac{2(x+2)}{(x+1)(x+3)} )( \frac{(x-2)(x+2)}{x+1} )\)=
\(( \frac{2(x+2)}{(x+1)(x+3)} )( \frac{x+1}{(x-2)(x+2)} )\)=
\(\frac{2(x+2)(x+1)}{(x+1)(x+3)(x-2)(x+2)}\)=
factor out ones
\(( \frac{2}{(x+3)(x-2)} )( \frac{(x+2)(x+1)}{(x+2)(x+1)} )\)=
\(( \frac{2}{(x+3)(x-2)} )(1)\)=
\(\frac{2}{(x+3)(x-2)}\)=
\(\frac{2}{x^2+x-6}\)
