Phân thức $\dfrac{{15}}{x}$ là kết quả của phép chia:

Ta có: $\dfrac{{5{x^2} - 20{y^2}}}{{3x + 6y}}:\dfrac{{5x - 10y}}{{9x}}$$= \dfrac{{5\left( {{x^2} - 4{y^2}} \right)}}{{3\left( {x + 2y} \right)}}.\dfrac{{9x}}{{5\left( {x - 2y} \right)}}$ $= \dfrac{{5\left( {x - 2y} \right)\left( {x + 2y} \right).9x}}{{3\left( {x + 2y} \right)5\left( {x - 2y} \right)}} = 15x$ nên A sai.

* $\dfrac{{45x - 90y}}{{3x + 6y}}:\dfrac{{{x^2} - 4{y^2}}}{{{x^2} + 4xy + 4{y^2}}}$ $= \dfrac{{45\left( {x - 2y} \right)}}{{3\left( {x + 2y} \right)}}.\dfrac{{{{\left( {x + 2y} \right)}^2}}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}$ $= \dfrac{{45\left( {x - 2y} \right){{\left( {x + 2y} \right)}^2}}}{{3{{\left( {x + 2y} \right)}^2}\left( {x - 2y} \right)}} = 15$ nên B sai.

* $\dfrac{{{x^2} - {y^2}}}{{2y}}:\left( {y - x} \right) = \dfrac{{\left( {x - y} \right)\left( {x + y} \right)}}{{2y}}.\dfrac{1}{{y - x}}$$= \dfrac{{\left( {x - y} \right)\left( {x + y} \right)}}{{2y}}.\dfrac{{ - 1}}{{x - y}} = \dfrac{{ - x - y}}{{2y}}$ nên C sai.