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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Which value of xx is an extraneous solution of xx−3=3x−3+2\dfrac{x}{x - 3} = \dfrac{3}{x - 3} + 2?

  • A

    x=−3x = -3

  • B

    x=3x = 3

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  • C

    x=0x = 0

  • D

    x=2x = 2

Explanation

Multiplying by x−3x - 3: x=3+2(x−3)=2x−3x = 3 + 2(x-3) = 2x - 3, so x=3x = 3. But this makes the denominator zero, so it is extraneous.

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