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Equivalent Expressions

SAT Math· difficulty 4/5

Which expression is equivalent to x2+5x+6x2−9÷x+2x−3\dfrac{x^2 + 5x + 6}{x^2 - 9} \div \dfrac{x + 2}{x - 3}?

  • A

    1x−3\dfrac{1}{x - 3}

  • B

    x+3x−3\dfrac{x + 3}{x - 3}

  • C

    11

    check_circle
  • D

    x+2x + 2

Explanation

(x+2)(x+3)(x−3)(x+3)⋅x−3x+2=(x+2)(x+3)(x−3)(x−3)(x+3)(x+2)=1\dfrac{(x+2)(x+3)}{(x-3)(x+3)} \cdot \dfrac{x-3}{x+2} = \dfrac{(x+2)(x+3)(x-3)}{(x-3)(x+3)(x+2)} = 1.

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