x2 - 1/ x-1 = -2What are all values of x that satisfy the equation above?
Correct answer: A. -3
- A. -3
- B. 0
- C. 1
- D. -3 and -1
Explanation
Choice A is correct. Factoring the numerator of the rational expression x2 − 1/ x − 1 yields (x + 1)(x − 1) / x − 1 . The expression (x + 1)(x − 1) / x − 1 can be rewritten as ( x + 1/ 1 )( x − 1/ x − 1. Since x−1 /x−1 = 1, when x is not equal to 1, it follows that (x+1/1)( x−1/x−1) = ( x + 1/1 )(1) or x + 1. Therefore, the given equation is equivalent to x + 1 = −2. Subtracting 1 from both sides of x + 1 = −2 yields x = −3.
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