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The values of x for which the expression above is NOT define
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12 Jun 2020, 10:56
12 Jun 2020, 10:56
Expert Reply
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Question Stats:
68% (00:44) correct
31% (00:51) wrong based on 35 sessions
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\(\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}\)
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
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
Re: The values of x for which the expression above is NOT define
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12 Jun 2020, 10:56
12 Jun 2020, 10:56
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: The values of x for which the expression above is NOT define
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12 Jun 2020, 12:30
12 Jun 2020, 12:30
Carcass wrote:
\(\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}\)
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
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 zero
So let's check each denominator individually and see what values of x make that denominator equal to zero.
If \(x^2 - 1 = 0\), then \(x^2 = 1\), which means \(x=1\) and \(x=-1\)
In other words, the expression is not defined when \(x=1\) and when \(x=-1\)
If \(x^2 - 4x + 4 = 0\), then we can factor the left side to get: \((x-2)(x-2)= 0\)
This means \(x = 2\)
So, 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
