$$\frac{ { a }^{ 2 \sqrt{ 2 } } - { b }^{ 2 \sqrt{ 2 } } }{ { \left( { a }^{ \sqrt{ 2 } } - { b }^{ \sqrt{ 3 } } \right) }^{ 2 } } +1$$
$\frac{-2a^{\sqrt{2}}b^{\sqrt{3}}+2a^{2\sqrt{2}}+b^{2\sqrt{3}}-b^{2\sqrt{2}}}{\left(a^{\sqrt{2}}-b^{\sqrt{3}}\right)^{2}}$
$\frac{2\sqrt{2}\left(a^{\sqrt{2}}b^{2\sqrt{2}}+b^{\sqrt{3}}a^{2\sqrt{2}}-2b^{\sqrt{3}}a^{2\sqrt{2}}\right)}{a\left(a^{\sqrt{2}}-b^{\sqrt{3}}\right)^{3}}$