Question

simplify : (2/ (√5 + √3 )) + (1/ (√3 + √2 )) - (1/ (√5 + √2 ))

pls pls pls answer my question fast

Answer 1

$\frac{2}{ \sqrt{3} + \sqrt{5} } + \frac{1}{ \sqrt{3} + \sqrt{2} } - \frac{1}{ \sqrt{5} + \sqrt{2} } \\ = \frac{2( \sqrt{5} - \sqrt{3} )}{( \sqrt{5} + \sqrt{3} )( \sqrt{5} - \sqrt{3} )} + \frac{( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} )} - \frac{( \sqrt{5} - \sqrt{2} )}{( \sqrt{5} + \sqrt{2} )( \sqrt{5} - \sqrt{2} )} \\ = \frac{2( \sqrt{5} - \sqrt{3)} }{5 - 3} + \frac{( \sqrt{3} - \sqrt{2} )}{3 - 2} - \frac{( \sqrt{5} - \sqrt{2} }{5 - 2} \\ = \frac{2}{2} ( \sqrt{5} - \sqrt{3} ) + \sqrt{3} - \sqrt{2} - \frac{ \sqrt{5} }{3} + \frac{ \sqrt{2} }{3} \\ = (\sqrt{5} - \frac{ \sqrt{5} }{3}) - ( \sqrt{2} - \frac{ \sqrt{2} }{3} ) \\ = \frac{2 \sqrt{5} }{3} - \frac{2 \sqrt{2} }{3} = ( \sqrt{5} - \sqrt{2} ) \times \frac{2}{3}$
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Answer 2

Answer:

(3+2)(3−2)(3−2)−(5+2)(5−2)(5−2)=5−32(5−3)+3−2(3−2)−5−2(5−2=22(5−3)+3−2−35+32=(5−35)−(2−32)=325−322=(5−2)×32