Answer :
[tex]\boxed{\blue{\underline{\underline{\pink{\LARGE{\mathfrak{Solution:-}}}}}}}[/tex]
[tex]\rm{Question\:given\:is: \dfrac{7\sqrt{3}}{\sqrt{10} + \sqrt{3}} - \dfrac{2\sqrt{5}}{\sqrt{6} - \sqrt{5}}}[/tex]
[tex]\mathfrak{\underline{Let's\:Rationalise!}}[/tex]
[tex]\rm{\leadsto\:\bigg(\dfrac{7\sqrt{3}}{\sqrt{10} + \sqrt{3}} \bigg) \times \dfrac{\sqrt{10} - \sqrt{3}}{ \sqrt{10} - \sqrt{3}}\bigg) - \bigg(\dfrac{2\sqrt{5}}{\sqrt{6} - \sqrt{5}} \times \dfrac{\sqrt{6} + \sqrt{5}}{\sqrt{6} + \sqrt{5}}\bigg)}[/tex]
[tex]\rm{\leadsto \bigg(\dfrac{7\sqrt{3}(\sqrt{10} - \sqrt{3})}{(\sqrt{10})^2 - (\sqrt{3})^2} \bigg) -\bigg( \dfrac{2\sqrt{5}(\sqrt{6} + \sqrt{5})}{(\sqrt{6})^2 - (\sqrt{5})^2}}[/tex]
[tex]\rm{\leadsto \bigg(\dfrac{7(\sqrt{30} + \sqrt{3}\times \sqrt{3}}{10 - 3}\bigg) - \bigg(\dfrac{2(\sqrt{30} + \sqrt{5} \times \sqrt{5})}{6 - 5}}[/tex]
[tex]\rm{\leadsto \sqrt{30} - 3 - 2\sqrt{30} - 5}[/tex]
[tex]\rm{\leadsto -\sqrt{30} - 8}[/tex]
[tex]\boxed{\underline{\overline{\bf{\blue{\large{Answer = - \sqrt{30} - 8}}}}}}[/tex]