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Answer:
[tex] \bf ➤ \underline{Solution-} \\ [/tex]
[tex] \sf \: \: \: \dfrac{1}{ 2 \sqrt{5} + \sqrt{3} } [/tex]
On rationalising,
[tex] \sf \implies\dfrac{1}{ 2 \sqrt{5} + \sqrt{3} } \times \dfrac{2 \sqrt{5} - \sqrt{3}}{2 \sqrt{5} - \sqrt{3}} [/tex]
Combine the fractions,
[tex] \sf \implies \dfrac{1(2 \sqrt{5} - \sqrt{3})}{(2 \sqrt{5} + \sqrt{3})(2 \sqrt{5} - \sqrt{3})} [/tex]
We know that,
[tex] \sf \implies (a + b)(a - b) = (a)^{2} - (b)^{2} [/tex]
So,
[tex] \sf \implies \dfrac{1(2 \sqrt{5} - \sqrt{3})}{(2 \sqrt{5} )^{2} - (\sqrt{3})^{2} } [/tex]
[tex] \sf \implies \dfrac{1(2 \sqrt{5} - \sqrt{3})}{20 - 3 } [/tex]
[tex] \sf \implies \dfrac{1(2 \sqrt{5} - \sqrt{3})}{17 } [/tex]
[tex] \sf \implies \dfrac{2 \sqrt{5} - \sqrt{3}}{17 } [/tex]
Hence,
On rationalising we got,
[tex] \bf \implies\dfrac{2 \sqrt{5} - \sqrt{3}}{17 } [/tex]