Chọn câu đúng.

* \(\dfrac{{3x - 4}}{{4{x^2}{y^5}}} + \dfrac{{9x + 4}}{{4{x^2}{y^5}}} = \dfrac{{3x - 4 + 9x + 4}}{{4{x^2}{y^5}}} = \dfrac{{12x}}{{4{x^2}{y^5}}} = \dfrac{3}{{x{y^5}}}\)  nên A sai.

* \(\dfrac{{2x + 5}}{3} + \dfrac{{x - 2}}{3} = \dfrac{{2x + 5 + x - 2}}{3} = \dfrac{{3x + 3}}{3} = x + 1\) nên B sai.

*

 \(\begin{array}{l}\,\,\,\,\dfrac{{x + 8}}{{x - 1}} - \dfrac{{2x - 1}}{{x - 1}} - \dfrac{{6x + 2}}{{x - 1}}\\ = \dfrac{{x + 8 - (2x - 1) - (6x + 2)}}{{x - 1}}\\ = \dfrac{{x + 8 - 2x + 1 - 6x - 2}}{{x - 1}}\\ = \dfrac{{ - 7x + 7}}{{x - 1}} = \dfrac{{ - 7(x - 1)}}{{x - 1}} =  - 7.\end{array}\)

nên C sai.

* \(\dfrac{x}{{x - y}} + \dfrac{y}{{x + y}} + \dfrac{{2{y^2}}}{{{x^2} - {y^2}}}\)\( = \dfrac{{x\left( {x + y} \right)}}{{\left( {x - y} \right)\left( {x + y} \right)}} + \dfrac{{y\left( {x - y} \right)}}{{\left( {x + y} \right)\left( {x - y} \right)}} + \dfrac{{2{y^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}}\) 

\( = \dfrac{{{x^2} + xy + xy - {y^2} + 2{y^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}}\)  \( = \dfrac{{{x^2} + {y^2} + 2xy}}{{\left( {x - y} \right)\left( {x + y} \right)}} = \dfrac{{{{\left( {x + y} \right)}^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}} = \dfrac{{x + y}}{{x - y}}\)  nên D đúng.