(a) Differentiate \(\frac{x^{2} + 1}{(x + 1)^{2}}\) with respect to x.

(b)(i) Evaluate \(\begin{vmatrix} 1 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}\).

(ii) Using the answer in (b)(i), solve the system of equations.

\(x + 2y - z = 4\)

\(2x + 3y - z = 2\)

\(-x + y + 3z = -1\).