For x > 2, which expression is equivalent to 1x + 2 + 1x - 2?

SAT Equivalent expressions Practice Question 11 (Medium)

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Math · Advanced MathMedium

For $x > 2$ , which expression is equivalent to $\frac{1}{x + 2} + \frac{1}{x - 2}$ ?

$\frac{2}{2x}$

$\frac{4}{x^2 - 4}$

$\frac{2}{x^2 - 4}$

$\frac{2x}{x^2 - 4}$

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Answer: D

Use the common denominator $(x + 2)(x - 2) = x^2 - 4$ : $\frac{(x - 2) + (x + 2)}{x^2 - 4} = \frac{2x}{x^2 - 4}$ .

Choice A adds the numerators and adds the denominators, which is not how fractions are added.

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