Three rational expressions are given: .

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

Problem

Three rational expressions are given:

\displaystyle p(x)=\frac{x}{x-3},\quad q(x)=\frac{x+5}{x^2-9},\quad r(x)=\frac{x^2-1}{x^2-4x+3}

. (i) Determine the set of excluded values for each of

p(x)

q(x)

and

r(x)

separately. (ii) Using your results from part (i), write the domain of

p(x)+q(x)

. (iii) Find the domain of the product

p(x)\,q(x)\,r(x)

, clearly indicating all values that must be excluded and giving reasons for each exclusion.