Subtract the following rational expressions and write the difference in simplest form if possible.
$\frac{x + 2}{x^{2} - 4} - \frac{1}{x - 2}$

$\frac{1}{(x - 2) (x + 2)}$

$\frac{x + 2}{(x - 2) (x + 2)}$

$\frac{x - 2}{(x - 2) (x + 2)}$

$0$

Verified step by step guidance

Identify the denominators of the rational expressions: the first denominator is $x^2 - 4$ and the second denominator is $x - 2$.

Factor the denominator $x^2 - 4$ as a difference of squares: $x^2 - 4 = (x - 2)(x + 2)$.

Rewrite both rational expressions with the common denominator $(x - 2)(x + 2)$: the first fraction remains $\frac{x+2}{(x-2)(x+2)}$, and the second fraction becomes $\frac{1}{x-2} = \frac{x+2}{(x-2)(x+2)}$ after multiplying numerator and denominator by $(x+2)$.

Set up the subtraction with the common denominator: $\frac{x+2}{(x-2)(x+2)} - \frac{x+2}{(x-2)(x+2)}$.

Subtract the numerators over the common denominator: $\frac{(x+2) - (x+2)}{(x-2)(x+2)}$, then simplify the numerator and denominator if possible.

6:23m

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Subtract the following rational expressions and write the difference in simplest form if possible.x+2x2−4−1x−2\(\frac{x+2}{x^2-4}\)-\(\frac{1}{x-2}\)

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Subtract the following rational expressions and write the difference in simplest form if possible.
$\frac{x + 2}{x^{2} - 4} - \frac{1}{x - 2}$