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\frac{\left(x^{2}+7x-18\right)\left(x^{2}+5x-24\right)}{\left(x^{2}+6x-27\right)\left(x^{2}+11x+24\right)}
Divide \frac{x^{2}+7x-18}{x^{2}+6x-27} by \frac{x^{2}+11x+24}{x^{2}+5x-24} by multiplying \frac{x^{2}+7x-18}{x^{2}+6x-27} by the reciprocal of \frac{x^{2}+11x+24}{x^{2}+5x-24}.
\frac{\left(x-3\right)\left(x-2\right)\left(x+8\right)\left(x+9\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)\left(x+9\right)}
Factor the expressions that are not already factored.
\frac{x-2}{x+3}
Cancel out \left(x-3\right)\left(x+8\right)\left(x+9\right) in both numerator and denominator.
\frac{\left(x^{2}+7x-18\right)\left(x^{2}+5x-24\right)}{\left(x^{2}+6x-27\right)\left(x^{2}+11x+24\right)}
Divide \frac{x^{2}+7x-18}{x^{2}+6x-27} by \frac{x^{2}+11x+24}{x^{2}+5x-24} by multiplying \frac{x^{2}+7x-18}{x^{2}+6x-27} by the reciprocal of \frac{x^{2}+11x+24}{x^{2}+5x-24}.
\frac{\left(x-3\right)\left(x-2\right)\left(x+8\right)\left(x+9\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)\left(x+9\right)}
Factor the expressions that are not already factored.
\frac{x-2}{x+3}
Cancel out \left(x-3\right)\left(x+8\right)\left(x+9\right) in both numerator and denominator.