Question

Simplify :

(7√3) / (√10 + √3) - ( 2√5) /( √6 + √5) - ( 3√2) / (√15 + 3√2)
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Answer 1

$\boxed{\ \: Question}$

Simplify -

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$\boxed{ \ \: Answer}$

$= \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$= \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} ) }{( \sqrt{10} + \sqrt{3} )( \sqrt{10} - \sqrt{3} ) } - \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{( \sqrt{6} + \sqrt{5})( \sqrt{6} - \sqrt{5} ) } - \frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} )}{( \sqrt{15} - 3 \sqrt{2} )( \sqrt{15} + 3 \sqrt{2}) }$

$= \frac{7 \sqrt{30} - 21}{( { \sqrt{10}) }^{2} - ( { \sqrt{3} )}^{2} } - \frac{2 \sqrt{30} - 10}{ ({ \sqrt{6}) }^{2} - {( \sqrt{5} )}^{2} } - \frac{3 \sqrt{30} - 18 }{ {( \sqrt{15}) }^{2} -( {3 \sqrt{2} )}^{2} }$

$= \frac{7 \sqrt{30} - 21}{10 - 3} - \frac{2 \sqrt{30} - 10}{6 - 5} - \frac{3 \sqrt{30} - 18}{15 - 18}$

$= \frac{7 \sqrt{30} - 21 }{7} - \frac{2 \sqrt{30} - 10}{1} - \frac{3 \sqrt{30} - 18}{ - 3}$

$= \sqrt{30} - 3 - (2 \sqrt{30} - 10) - ( - \sqrt{30} + 6)$

$= \sqrt{30} - 3 - 2 \sqrt{30} + 10 + \sqrt{30} - 6$

$= 2 \sqrt{30} - 2 \sqrt{30} - 3 + 10 - 6$

$= - 3 - 6 + 10$

$= - 9 + 10$

$= 1$

Answer 2

Answer:

This is answer of question