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Equivalent Expressions

SAT Math· difficulty 5/5

Which expression is equivalent to 1x+1y1x−1y\dfrac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}?

  • A

    x+yx−y\dfrac{x + y}{x - y}

  • B

    y+xy−x\dfrac{y + x}{y - x}

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  • C

    1x−y\dfrac{1}{x - y}

  • D

    xy+1xy−1\dfrac{xy + 1}{xy - 1}

Explanation

Multiply numerator and denominator by xyxy: y+xy−x\dfrac{y + x}{y - x}.

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