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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

Solve for xx: x+4x2−16=1x−4\dfrac{x + 4}{x^2 - 16} = \dfrac{1}{x - 4}

  • A

    x=−4x = -4

  • B

    All real xx except x=±4x = \pm 4

    check_circle
  • C

    x=0x = 0

  • D

    x=4x = 4

Explanation

LHS =x+4(x−4)(x+4)=1x−4= \dfrac{x + 4}{(x-4)(x+4)} = \dfrac{1}{x - 4} (for x≠−4x \ne -4). So the equation is an identity for all xx except ±4\pm 4.

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