For x > 3, which expression is equivalent to 2x - 3 - 12x^2 - 9?

SAT Equivalent expressions Practice Question 20 (Hard)

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For $x > 3$ , which expression is equivalent to $\frac{2}{x - 3} - \frac{12}{x^2 - 9}$ ?

$\frac{2}{x + 3}$

$\frac{-10}{x^2 - 9}$

$\frac{2}{x - 3}$

$\frac{2x + 18}{x^2 - 9}$

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Answer: A

The common denominator is $x^2 - 9 = (x - 3)(x + 3)$ . Rewrite: $\frac{2(x + 3) - 12}{x^2 - 9} = \frac{2x - 6}{(x - 3)(x + 3)} = \frac{2(x - 3)}{(x - 3)(x + 3)} = \frac{2}{x + 3}$ .

Choice B subtracts the numerators without first rewriting $\frac{2}{x - 3}$ over the common denominator.

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