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Equivalent Expressions

SAT Math· difficulty 4/5

Which expression is equivalent to xx2−1+1x−1\dfrac{x}{x^2 - 1} + \dfrac{1}{x - 1}?

  • A

    Both A and C

  • B

    x+1(x−1)(x+1)\dfrac{x + 1}{(x-1)(x+1)}

  • C

    2x+1(x−1)(x+1)\dfrac{2x + 1}{(x-1)(x+1)}

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  • D

    2x+1x2−1\dfrac{2x + 1}{x^2 - 1}

Explanation

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

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