Answer:
[tex] \longmapsto \sqrt{7 } + \sqrt{2} .[/tex]
Step-by-step explanation:
[tex]\sf{\:\dfrac{5}{\sqrt{7} - \sqrt{2}}}[/tex]
By rationalizing the denominator,
[tex]=\sf{\dfrac{5}{\sqrt{7} - \sqrt{2}}\times \dfrac{\sqrt{7} + \sqrt{2}}{\sqrt{7} + \sqrt{7}}}[/tex]
[tex]=\sf{\dfrac{5(\sqrt{7} + \sqrt{2})}{(\sqrt{7} - \sqrt{2})(\sqrt{7} + \sqrt{2})}}[/tex]
[tex]=\sf{\dfrac{5(\sqrt{7} + \sqrt{2})}{(\sqrt{7})^2 - (\sqrt{2})^2}}[/tex]
[tex]=\sf{\dfrac{5(\sqrt{7} + \sqrt{2})}{7 - 2}}[/tex]
[tex]=\sf{\dfrac{5(\sqrt{7} + \sqrt{2})}{5}}[/tex]
[tex]=\sf{\dfrac{\not{5}(\sqrt{7} + \sqrt{2})}{\not{5}}}[/tex]
[tex]\boxed{\underline{\rm{\therefore\:\dfrac{5}{\sqrt{7} - \sqrt{2}} = \sqrt{7} + \sqrt{2}}}}[/tex]
