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\frac{\left(3x-4y\right)\left(3x+4y\right)^{2}}{9x^{2}+24xy+16y^{2}}
Divide \frac{3x-4y}{9x^{2}+24xy+16y^{2}} by \frac{1}{\left(3x+4y\right)^{2}} by multiplying \frac{3x-4y}{9x^{2}+24xy+16y^{2}} by the reciprocal of \frac{1}{\left(3x+4y\right)^{2}}.
\frac{\left(3x-4y\right)\left(3x+4y\right)^{2}}{\left(3x+4y\right)^{2}}
Factor the expressions that are not already factored.
3x-4y
Cancel out \left(3x+4y\right)^{2} in both numerator and denominator.
\frac{\left(3x-4y\right)\left(3x+4y\right)^{2}}{9x^{2}+24xy+16y^{2}}
Divide \frac{3x-4y}{9x^{2}+24xy+16y^{2}} by \frac{1}{\left(3x+4y\right)^{2}} by multiplying \frac{3x-4y}{9x^{2}+24xy+16y^{2}} by the reciprocal of \frac{1}{\left(3x+4y\right)^{2}}.
\frac{\left(3x-4y\right)\left(3x+4y\right)^{2}}{\left(3x+4y\right)^{2}}
Factor the expressions that are not already factored.
3x-4y
Cancel out \left(3x+4y\right)^{2} in both numerator and denominator.