Question

please solve this and if possible write in copie​

Answer 1

${\implies\sf\cfrac{1}{2 + \sqrt{3} } + \cfrac{2}{ \sqrt{5} - 3} + \cfrac{1}{2 - \sqrt{5} }}$

${\implies \sf\cfrac{1(2 - \sqrt{3} )}{(2 + \sqrt{3})(2 - \sqrt{3} ) } + \cfrac{2( \sqrt{5} + 3) }{ (\sqrt{5} - 3)( \sqrt{5} + 3) } + \cfrac{1(2 + \sqrt{5} }{(2 - \sqrt{5})(2 + \sqrt{5} )}}$

${\implies\sf\cfrac{2 - \sqrt{3} }{ {2}^{2} - (\sqrt{3}) ^{2} } + \cfrac{2 \sqrt{5} + 6}{ ( \sqrt{5})^{2} - {3}^{2} } + \cfrac{1(2 + \sqrt{5} }{ {2}^{2} -( \sqrt{5} ) ^{2}} }$

${\implies\sf\cfrac{2 - \sqrt{3} }{4 - 3 } + \cfrac{2 \sqrt{5} + 6}{ 5 - 9 } + \cfrac{2 + \sqrt{5} }{ 4 - 5 }}$

${\sf\implies\cfrac{2 - \sqrt{3} }{1 } + \cfrac{2 (\sqrt{5} + 3)}{ - 4 } + \cfrac{2 + \sqrt{5} }{ - 1 }}$

$\sf{\implies \cancel{2} - \sqrt{3} }{ } - \cfrac{ \cancel{2}( \sqrt{5} + 3)}{ \cancel{ 4 }^{2} } - {\cancel{2} + \sqrt{5} }$

$\sf \implies - \sqrt{3} + \sqrt{5} - \cfrac{ \sqrt{5} + 3}{ 2 }$

$\sf \implies \dfrac{ - \sqrt{ 3}} {1} + \dfrac{\sqrt{5}}{1} - \cfrac{ \sqrt{5} + 3}{ 2 }$

$\sf \implies \dfrac{ - \sqrt{ 3} \times 2 + 2 \times \sqrt{5} - 2 \times \sqrt{5} + 3 \times 2 } {2}$

$\sf \implies \dfrac{ -2 \sqrt{3} + 2\sqrt{5} - 2\sqrt{5} + 6} {2}$

$\sf \implies \dfrac{ -2 \sqrt{3} + \xcancel{2\sqrt{5} } - \xcancel{2\sqrt{5}} + 6} {2}$

$\sf \implies \dfrac{ 2 ( - \sqrt{3} + 3)} {2}$

$\sf \implies 3 - \sqrt{3}$

Hope it helpful ❣️

Answer 2

Answer:

3-√3

Step-by-step explanation:

answer is in the attachment