$$\frac{x(2x+3y)}{3x+y}\times\frac{4x^{2}-9y^{2}}{4x^{3}-9xy^{2}}$$
$\frac{2x+3y}{3x+y}$
$$\frac{2x^{2}+3xy}{3x+y}\times \frac{4x^{2}-9y^{2}}{4x^{3}-9xy^{2}}$$
$$\frac{2x^{2}+3xy}{3x+y}\times \frac{\left(2x-3y\right)\left(2x+3y\right)}{x\left(2x-3y\right)\left(2x+3y\right)}$$
$$\frac{2x^{2}+3xy}{3x+y}\times \frac{1}{x}$$
$$\frac{2x^{2}+3xy}{\left(3x+y\right)x}$$
$$\frac{x\left(2x+3y\right)}{x\left(3x+y\right)}$$
$$\frac{2x+3y}{3x+y}$$
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