$$\frac{2x^{2}-12x-54}{2x+14}\div(4x+12)=$$
$\frac{x-9}{4\left(x+7\right)}$
$$\frac{2x^{2}-12x-54}{\left(2x+14\right)\left(4x+12\right)}$$
$$\frac{2\left(x-9\right)\left(x+3\right)}{2\times 4\left(x+3\right)\left(x+7\right)}$$
$$\frac{x-9}{4\left(x+7\right)}$$
$$\frac{x-9}{4x+28}$$
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