Khi rút gọn biểu thức \(\dfrac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\dfrac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\) , ta được kết quả là
\(-\dfrac{5\sqrt{2}}{4}\). \(\dfrac{5\sqrt{2}}{4}\). \(\dfrac{\sqrt{2}}{4}\). \(-\dfrac{\sqrt{2}}{4}\). Hướng dẫn giải:\(\dfrac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\dfrac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\)
\(=\dfrac{5\left(2\sqrt{5}-3\sqrt{2}\right)}{12\left(2\sqrt{5}+3\sqrt{2}\right)\left(2\sqrt{5}-3\sqrt{2}\right)}-\dfrac{5\left(2\sqrt{5}+3\sqrt{2}\right)}{12\left(2\sqrt{5}+3\sqrt{2}\right)\left(2\sqrt{5}-3\sqrt{2}\right)}\)
\(=\dfrac{10\sqrt{5}-15\sqrt{2}-10\sqrt{5}-15\sqrt{2}}{12.\left(20-18\right)}\)
\(=\dfrac{-30\sqrt{2}}{24}=\dfrac{-5\sqrt{2}}{4}\)