Rút gọn \(\dfrac{2}{{{x^2} - {y^2}}}\sqrt {\dfrac{{3{{\left( {x + y} \right)}^2}}}{2}} \) với \(x \ge 0;\,\,y \ge 0;\,\,x \ne y\)

* Hướng dẫn giải

\(\dfrac{2}{{{x^2} - {y^2}}}\sqrt {\dfrac{{3{{\left( {x + y} \right)}^2}}}{2}} \)\( = \dfrac{{2\left| {x + y} \right|}}{{{x^2} - {y^2}}}\sqrt {\dfrac{3}{2}} \)\( = \dfrac{{x + y}}{{\left( {x + y} \right)\left( {x - y} \right)}}\sqrt {\dfrac{{{2^2}.3}}{2}} \) \( = \dfrac{{\sqrt 6 }}{{x - y}}\)  (vì \(x + y > 0\) nên \(\left| {x + y} \right| = x + y\))