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Equivalent Expressions

SAT Math· difficulty 4/5

Which is equivalent to x3−8x2−4\dfrac{x^3 - 8}{x^2 - 4} for x≠2,−2x \ne 2, -2?

  • A

    x2−2x+4x+2\dfrac{x^2 - 2x + 4}{x + 2}

  • B

    x+2x−2\dfrac{x + 2}{x - 2}

  • C

    x−2x - 2

  • D

    x2+2x+4x+2\dfrac{x^2 + 2x + 4}{x + 2}

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Explanation

(x−2)(x2+2x+4)(x−2)(x+2)=x2+2x+4x+2\dfrac{(x-2)(x^2 + 2x + 4)}{(x-2)(x+2)} = \dfrac{x^2 + 2x + 4}{x + 2}.

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