Let and be rational functions

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

p(x)

and

q(x)

be rational functions. Consider

r(x)=\dfrac{p(x)}{q(x)}

. Which of the following always describes the domain of

r

? (a) All real

x

for which

q(x)\ne0

(b) All real

x

for which

p(x)\ne0

and

q(x)\ne0

x

for which both

p(x)

and

q(x)

are defined and

q(x)\ne0

(d) All real

x

except those for which either

p(x)=0

q(x)=0