\( y = \frac { x ^ { 2 } + 1 } { x - 1 } - 3 x ; y ^ { \prime \prime } \)

To solve for \( y'' \) given the function \( y = \frac { x ^ { 2 } + 1 } { x - 1 } - 3 x \), we first need to find the first derivative \( y' \). After applying the quotient rule to differentiate the first term and simplifying, we can then find the second derivative \( y'' \). Once we have \( y' \), we again differentiate using similar rules, ensuring we keep track of the product and quotient rules as necessary. Be sure to simplify the final expression for \( y'' \) as needed! The journey of derivatives can be quite the ride, so be prepared to manipulate those algebraic expressions and perhaps even break out the chain rule if you encounter any composite functions along the way!