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Equivalent Expressions

SAT Math· difficulty 4/5

Which expression is equivalent to 2x2−5x−3x2−9\dfrac{2x^2 - 5x - 3}{x^2 - 9} for x≠±3x \ne \pm 3?

  • A

    2x+12x + 1

  • B

    2x+1x−3\dfrac{2x + 1}{x - 3}

  • C

    2x−1x+3\dfrac{2x - 1}{x + 3}

  • D

    2x+1x+3\dfrac{2x + 1}{x + 3}

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Explanation

Numerator: 2x2−5x−3=(2x+1)(x−3)2x^2 - 5x - 3 = (2x + 1)(x - 3). Denominator: (x−3)(x+3)(x-3)(x+3). Cancel: 2x+1x+3\dfrac{2x + 1}{x + 3}.

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