Consider the function

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

Problem

f(x)=\dfrac{x^{2}+ax+b}{(x-1)(x^{2}+bx+a)}

, where

a

and

b

are real constants. The domain of

f

must exclude only

x=1

and no other real number. Which of the following ordered pairs

(a,b)

satisfies this condition? (a)

(2,3)

(b)

(2,1)

(c)

(1,2)

(d)

(-1,0)