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Equivalent Expressions

SAT Math· difficulty 5/5

Which is equivalent to x3−27x2−9\frac{x^3 - 27}{x^2 - 9}?

  • A

    x−3x+3\frac{x - 3}{x + 3}

  • B

    x2−3x+9x−3\frac{x^2 - 3x + 9}{x - 3}

  • C

    x2+3x^2 + 3

  • D

    x2+3x+9x+3\frac{x^2 + 3x + 9}{x + 3}

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Explanation

(x−3)(x2+3x+9)(x−3)(x+3)=x2+3x+9x+3\frac{(x - 3)(x^2 + 3x + 9)}{(x - 3)(x + 3)} = \frac{x^2 + 3x + 9}{x + 3} (for x≠3x \neq 3).

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