Using Differentiation to Evaluate Functions - If y=(x-1)/(x+1) evaluate (x+1)(d²y/dx²)+2(dy/dx)

Learn to apply differentiation methods to evaluate complex mathematical expressions through a step-by-step solution of the problem: given y=(x-1)/(x+1), evaluate (x+1)(d²y/dx²)+2(dy/dx). Master the techniques for finding first and second derivatives of rational functions, then substitute these derivatives into the given expression to arrive at the final answer. Develop proficiency in quotient rule application, algebraic manipulation of derivatives, and systematic problem-solving approaches for calculus evaluation problems involving rational functions and their higher-order derivatives.