Which solution to the equation the fraction with numerator 1 and denominator x minus 1 is equal to the fraction with numerator x minus 2 and denominator 2 x squared minus 2 is extraneous?

The denominators are zero when x = 1 or x = −1, so those values cannot be solutions to the original equation. Cross-multiplying gives 2x² − 2 = (x − 2)(x − 1), which simplifies to x² + 3x − 4 = 0, or (x + 4)(x − 1) = 0. The resulting candidates are x = −4 and x = 1; since x = 1 makes a denominator zero, it is extraneous. The correct choice is x = 1.

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