Evaluate
-\frac{24xy}{4x^{2}-9y^{2}}
Expand
-\frac{24xy}{4x^{2}-9y^{2}}
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\frac{\left(2x-3y\right)\left(2x-3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}-\frac{\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+3y and 2x-3y is \left(2x-3y\right)\left(2x+3y\right). Multiply \frac{2x-3y}{2x+3y} times \frac{2x-3y}{2x-3y}. Multiply \frac{2x+3y}{2x-3y} times \frac{2x+3y}{2x+3y}.
\frac{\left(2x-3y\right)\left(2x-3y\right)-\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}
Since \frac{\left(2x-3y\right)\left(2x-3y\right)}{\left(2x-3y\right)\left(2x+3y\right)} and \frac{\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-6xy-6xy+9y^{2}-4x^{2}-6xy-6xy-9y^{2}}{\left(2x-3y\right)\left(2x+3y\right)}
Do the multiplications in \left(2x-3y\right)\left(2x-3y\right)-\left(2x+3y\right)\left(2x+3y\right).
\frac{-24xy}{\left(2x-3y\right)\left(2x+3y\right)}
Combine like terms in 4x^{2}-6xy-6xy+9y^{2}-4x^{2}-6xy-6xy-9y^{2}.
\frac{-24xy}{4x^{2}-9y^{2}}
Expand \left(2x-3y\right)\left(2x+3y\right).
\frac{\left(2x-3y\right)\left(2x-3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}-\frac{\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+3y and 2x-3y is \left(2x-3y\right)\left(2x+3y\right). Multiply \frac{2x-3y}{2x+3y} times \frac{2x-3y}{2x-3y}. Multiply \frac{2x+3y}{2x-3y} times \frac{2x+3y}{2x+3y}.
\frac{\left(2x-3y\right)\left(2x-3y\right)-\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}
Since \frac{\left(2x-3y\right)\left(2x-3y\right)}{\left(2x-3y\right)\left(2x+3y\right)} and \frac{\left(2x+3y\right)\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x^{2}-6xy-6xy+9y^{2}-4x^{2}-6xy-6xy-9y^{2}}{\left(2x-3y\right)\left(2x+3y\right)}
Do the multiplications in \left(2x-3y\right)\left(2x-3y\right)-\left(2x+3y\right)\left(2x+3y\right).
\frac{-24xy}{\left(2x-3y\right)\left(2x+3y\right)}
Combine like terms in 4x^{2}-6xy-6xy+9y^{2}-4x^{2}-6xy-6xy-9y^{2}.
\frac{-24xy}{4x^{2}-9y^{2}}
Expand \left(2x-3y\right)\left(2x+3y\right).
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