AP

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

R(x)=\dfrac{2x^2-8}{x^3-x^2-6x}

. (i) Completely factorise both the numerator and the denominator of

R(x)

. (ii) Solve the equation obtained from setting the denominator equal to zero and list all excluded values for

R(x)

. (iii) Hence write the domain of

R(x)

in set-builder form. (iv) Simplify

R(x)

as far as possible and state whether any of the excluded values found in part (ii) can be removed after simplification.