Mathematics

Problem

A function is defined as

g(x) = \dfrac{x^{3} + 2x - 1}{x^{2} - x - 2}, \quad x \ne 1,\,-2.

Answer the following parts. a. Part 1: (a) Find

g'(x)

and simplify the result as far as possible. b. Part 2: (b) Determine the equation of the tangent to the curve

y = g(x)

at the point where

x = 3