[tex]= (-1)^k \cdot \sqrt{\dfrac{9}{2} } - (-1)^k \cdot \sqrt{\dfrac{16}{3} } = (-1)^k \cdot \dfrac{3}{\sqrt{2}} - (-1)^k \cdot \dfrac{4}{\sqrt{3}}[/tex]
[tex]= (-1)^k \cdot \dfrac{3\sqrt{2}}{2} - (-1)^k \cdot \dfrac{4\sqrt{3}}{3} = (-1)^k \cdot \dfrac{9\sqrt{2}}{6} - (-1)^k \cdot \dfrac{8\sqrt{3}}{6}[/tex]
[tex]= (-1)^k \cdot \dfrac{9\sqrt{2} - 8\sqrt{3}}{6}[/tex]
