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Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to 2x−1+3x+1\dfrac{2}{x - 1} + \dfrac{3}{x + 1}?

  • A

    5x−1x2−1\dfrac{5x - 1}{x^2 - 1}

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  • B

    5x+1x2−1\dfrac{5x + 1}{x^2 - 1}

  • C

    6x2−1\dfrac{6}{x^2 - 1}

  • D

    5x2−1\dfrac{5}{x^2 - 1}

Explanation

Common denominator (x−1)(x+1)=x2−1(x-1)(x+1) = x^2 - 1: 2(x+1)+3(x−1)x2−1=5x−1x2−1\dfrac{2(x+1) + 3(x-1)}{x^2 - 1} = \dfrac{5x - 1}{x^2 - 1}.

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