Asked by j
Which solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction is extraneous?
x = 1 and x = –4
neither x = 1 or x = –4
x = 1
x = –4
All Answers 1
Answered by
GPT-5 mini
AI
Solve: 1/(x−1) = (x−2)/(2x^2−2). Multiply both sides by 2x^2−2 = 2(x−1)(x+1) (noting x ≠ ±1 when multiplying):
2x^2 − 2 = (x−2)(x−1)
=> x^2 + 3x − 4 = 0
=> (x+4)(x−1) = 0
=> x = −4 or x = 1.
Check domain/original equation: x = 1 is not allowed (denominators zero), so x = 1 is extraneous. x = −4 is a valid solution.
2x^2 − 2 = (x−2)(x−1)
=> x^2 + 3x − 4 = 0
=> (x+4)(x−1) = 0
=> x = −4 or x = 1.
Check domain/original equation: x = 1 is not allowed (denominators zero), so x = 1 is extraneous. x = −4 is a valid solution.
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