Evaluate
-\frac{12AB}{9A^{2}-B^{2}}
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-\frac{12AB}{9A^{2}-B^{2}}
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\frac{\left(3A-B\right)\left(3A-B\right)}{\left(3A+B\right)\left(3A-B\right)}-\frac{\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3A+B and 3A-B is \left(3A+B\right)\left(3A-B\right). Multiply \frac{3A-B}{3A+B} times \frac{3A-B}{3A-B}. Multiply \frac{3A+B}{3A-B} times \frac{3A+B}{3A+B}.
\frac{\left(3A-B\right)\left(3A-B\right)-\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)}
Since \frac{\left(3A-B\right)\left(3A-B\right)}{\left(3A+B\right)\left(3A-B\right)} and \frac{\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9A^{2}-3AB-3AB+B^{2}-9A^{2}-3AB-3AB-B^{2}}{\left(3A+B\right)\left(3A-B\right)}
Do the multiplications in \left(3A-B\right)\left(3A-B\right)-\left(3A+B\right)\left(3A+B\right).
\frac{-12AB}{\left(3A+B\right)\left(3A-B\right)}
Combine like terms in 9A^{2}-3AB-3AB+B^{2}-9A^{2}-3AB-3AB-B^{2}.
\frac{-12AB}{9A^{2}-B^{2}}
Expand \left(3A+B\right)\left(3A-B\right).
\frac{\left(3A-B\right)\left(3A-B\right)}{\left(3A+B\right)\left(3A-B\right)}-\frac{\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3A+B and 3A-B is \left(3A+B\right)\left(3A-B\right). Multiply \frac{3A-B}{3A+B} times \frac{3A-B}{3A-B}. Multiply \frac{3A+B}{3A-B} times \frac{3A+B}{3A+B}.
\frac{\left(3A-B\right)\left(3A-B\right)-\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)}
Since \frac{\left(3A-B\right)\left(3A-B\right)}{\left(3A+B\right)\left(3A-B\right)} and \frac{\left(3A+B\right)\left(3A+B\right)}{\left(3A+B\right)\left(3A-B\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9A^{2}-3AB-3AB+B^{2}-9A^{2}-3AB-3AB-B^{2}}{\left(3A+B\right)\left(3A-B\right)}
Do the multiplications in \left(3A-B\right)\left(3A-B\right)-\left(3A+B\right)\left(3A+B\right).
\frac{-12AB}{\left(3A+B\right)\left(3A-B\right)}
Combine like terms in 9A^{2}-3AB-3AB+B^{2}-9A^{2}-3AB-3AB-B^{2}.
\frac{-12AB}{9A^{2}-B^{2}}
Expand \left(3A+B\right)\left(3A-B\right).
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