A function is defined as Answer the following parts.

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A function is defined as g(x)=x3+2x−1x2−x−2,x≠1, −2.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)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)y = g(x) at the point where x=3x = 3.

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