Which of the following expressions is equivalent to \(\dfrac{1}{x-a}-\dfrac{1}{x+a}\) ?
\(\dfrac{2a}{x^2-a^2}\)
\(\dfrac{a^2}{x^2-a^2}\)
\(\dfrac{2x}{x^2-a^2}\)
\(\dfrac{1}{x^2-a^2}\)
\(-\dfrac{1}{2a}\)
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$$ \frac{1}{x-a}-\frac{1}{x+a} $$ $$ =\frac{x+a}{(x-a)(x+a)} - \frac{x-a}{(x+a)(x-a)} $$ $$ = \frac{x+a -(x-a)}{(x-a)(x+a)} $$ $$ =\boxed{\frac{2a}{x^2-a^2}} $$