Answer:
[tex] \longmapsto \: \sqrt{5} - \sqrt{2.} [/tex]
Step-by-step explanation:
[tex]\sf{\dfrac{3}{\sqrt{5} + \sqrt{2}}}[/tex]
By rationalizing the denominator,
[tex]=\sf{\dfrac{3}{\sqrt{5} + \sqrt{2}} \times \dfrac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}}[/tex]
[tex]=\sf{\dfrac{3(\sqrt{5} - \sqrt{2})}{(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})}}[/tex]
Applying the identity in the denominator:-
[tex]\boxed{\underline{\red{\rm{(a + b)(a - b) = a^2 - b^2}}}}[/tex]
[tex]=\sf{\dfrac{3(\sqrt{5} - \sqrt{2})}{(\sqrt{5})^2 - (\sqrt{2})^2}}[/tex]
[tex]=\sf{\dfrac{3(\sqrt{5} - \sqrt{2})}{5 - 2}}[/tex]
[tex]=\sf{\dfrac{3(\sqrt{5} - \sqrt{2})}{3}}[/tex]
[tex]=\sf{\dfrac{\not{3}(\sqrt{5} - \sqrt{2})}{\not{3}}}[/tex]
[tex]\blue{\boxed{\underline{\rm{\therefore\:\dfrac{3}{\sqrt{5} + \sqrt{2}} = \sqrt{5} - \sqrt{2}}}}}[/tex]
