Carcass wrote:
x+1x2−1−x−2x2−4x+4
The values of x for which the expression above is NOT defined are
A. 1 and 2 only
B. –1 and 2 only
C. –1 and –2 only
D. –1, 1, and –2
E. –1, 1, and 2
Key concept: A rational expression (aka fraction) is undefined when the denominator equal zeroSo let's check each denominator individually and see what values of x make that denominator equal to zero.
If
x2−1=0, then
x2=1, which means
x=1 and
x=−1In other words, the expression is not defined when
x=1 and when
x=−1If
x2−4x+4=0, then we can factor the left side to get:
(x−2)(x−2)=0This means
x=2So, the expression is not defined when
x=2 So the expression is undefined when
x=1,
x=−1 and
x=2 Answer: E
Cheers,
Brent