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\frac{\left(x^{2}-3x-18\right)\left(-2x\right)^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Divide \frac{x^{2}-3x-18}{x^{2}-6x} by \frac{6x^{2}+18}{\left(-2x\right)^{2}} by multiplying \frac{x^{2}-3x-18}{x^{2}-6x} by the reciprocal of \frac{6x^{2}+18}{\left(-2x\right)^{2}}.
\frac{\left(x^{2}-3x-18\right)\left(-2\right)^{2}x^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Expand \left(-2x\right)^{2}.
\frac{\left(x^{2}-3x-18\right)\times 4x^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Calculate -2 to the power of 2 and get 4.
\frac{4\left(x-6\right)\left(x+3\right)x^{2}}{6x\left(x-6\right)\left(x^{2}+3\right)}
Factor the expressions that are not already factored.
\frac{2x\left(x+3\right)}{3\left(x^{2}+3\right)}
Cancel out 2x\left(x-6\right) in both numerator and denominator.
\frac{2x^{2}+6x}{3x^{2}+9}
Expand the expression.
\frac{\left(x^{2}-3x-18\right)\left(-2x\right)^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Divide \frac{x^{2}-3x-18}{x^{2}-6x} by \frac{6x^{2}+18}{\left(-2x\right)^{2}} by multiplying \frac{x^{2}-3x-18}{x^{2}-6x} by the reciprocal of \frac{6x^{2}+18}{\left(-2x\right)^{2}}.
\frac{\left(x^{2}-3x-18\right)\left(-2\right)^{2}x^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Expand \left(-2x\right)^{2}.
\frac{\left(x^{2}-3x-18\right)\times 4x^{2}}{\left(x^{2}-6x\right)\left(6x^{2}+18\right)}
Calculate -2 to the power of 2 and get 4.
\frac{4\left(x-6\right)\left(x+3\right)x^{2}}{6x\left(x-6\right)\left(x^{2}+3\right)}
Factor the expressions that are not already factored.
\frac{2x\left(x+3\right)}{3\left(x^{2}+3\right)}
Cancel out 2x\left(x-6\right) in both numerator and denominator.
\frac{2x^{2}+6x}{3x^{2}+9}
Expand the expression.