Chapter A, Problem 47E

To determine

To calculate: The simplest form of the expression $\frac{-2{\left(x^2-3\right)}^{-3}\left(2x\right){\left(x+1\right)}^3-3{\left(x+1\right)}^2{\left(x^2-3\right)}^{-2}}{{\left[{\left(x+1\right)}^3\right]}^2}$.