[tex]L=\frac{a^{2\sqrt{2}}-b^{2\sqrt{3}}}{(a^{\sqrt{2}}-b^{\sqrt{3}})^2}+1=\frac{(a^{\sqrt{2}}-b^{\sqrt{3}})(a^{\sqrt{2}}+b^{\sqrt{3}})}{(a^{\sqrt{2}}-b^{\sqrt{3}})^2}+1=\frac{a^{\sqrt{2}}+b^{\sqrt{3}}}{a^{\sqrt{2}}-b^{\sqrt{3}}}+1=\frac{2a^{\sqrt{2}}}{a^{\sqrt{2}}-b^{\sqrt{3}}}[/tex]