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\frac{\left(x^{2}-9\right)\times 2}{\left(4x-12\right)\left(x+3\right)}
Divide \frac{x^{2}-9}{4x-12} by \frac{x+3}{2} by multiplying \frac{x^{2}-9}{4x-12} by the reciprocal of \frac{x+3}{2}.
\frac{2\left(x-3\right)\left(x+3\right)}{4\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{1}{2}
Cancel out 2\left(x-3\right)\left(x+3\right) in both numerator and denominator.