[tex]\displaystyle\bf\\\frac{4x^{3} y^{2} }{x-2} :2xy^{2} =\frac{4x^{3} y^{2} }{x-2} \cdot\frac{1}{2xy^{2} } =\frac{2xy^{2} \cdot 2x^{2} }{(x-2)\cdot 2xy^{2} } =\frac{2x^{2} }{x-2}[/tex]
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[tex]\displaystyle\bf\\\frac{4x^{3} y^{2} }{x-2} :2xy^{2} =\frac{4x^{3} y^{2} }{x-2} \cdot\frac{1}{2xy^{2} } =\frac{2xy^{2} \cdot 2x^{2} }{(x-2)\cdot 2xy^{2} } =\frac{2x^{2} }{x-2}[/tex]