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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Solve for xx: 1x−1−2x+1=2x2−1\dfrac{1}{x - 1} - \dfrac{2}{x + 1} = \dfrac{2}{x^2 - 1}

  • A

    x=−1x = -1

  • B

    x=1x = 1

  • C

    x=0x = 0

  • D

    x=−1x = -1 is extraneous; no valid solution

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Explanation

Multiply by x2−1x^2 - 1: (x+1)−2(x−1)=2⇒−x+3=2⇒x=1(x+1) - 2(x-1) = 2 \Rightarrow -x + 3 = 2 \Rightarrow x = 1. But x=1x = 1 makes a denominator zero, so it is extraneous. No valid solution.

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