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Differentiate w.r.t. x
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\frac{x+3}{\left(x-3\right)\left(x+3\right)}-\frac{x-3}{\left(x-3\right)\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{1}{x-3} times \frac{x+3}{x+3}. Multiply \frac{1}{x+3} times \frac{x-3}{x-3}.
\frac{x+3-\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}
Since \frac{x+3}{\left(x-3\right)\left(x+3\right)} and \frac{x-3}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-x+3}{\left(x-3\right)\left(x+3\right)}
Do the multiplications in x+3-\left(x-3\right).
\frac{6}{\left(x-3\right)\left(x+3\right)}
Combine like terms in x+3-x+3.
\frac{6}{x^{2}-9}
Expand \left(x-3\right)\left(x+3\right).