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\frac{2x^{2}+16x+24}{3x^{2}\left(2x+4\right)}
Express \frac{\frac{2x^{2}+16x+24}{3x^{2}}}{2x+4} as a single fraction.
\frac{2\left(x+2\right)\left(x+6\right)}{2\times 3\left(x+2\right)x^{2}}
Factor the expressions that are not already factored.
\frac{x+6}{3x^{2}}
Cancel out 2\left(x+2\right) in both numerator and denominator.
\frac{2x^{2}+16x+24}{3x^{2}\left(2x+4\right)}
Express \frac{\frac{2x^{2}+16x+24}{3x^{2}}}{2x+4} as a single fraction.
\frac{2\left(x+2\right)\left(x+6\right)}{2\times 3\left(x+2\right)x^{2}}
Factor the expressions that are not already factored.
\frac{x+6}{3x^{2}}
Cancel out 2\left(x+2\right) in both numerator and denominator.