Question

1. Simplify: (7√3 / √10+ √3) − (2√5 / √√6+√5) − (3√2 / √15+3√2)

Please explain it

Thank you

Answer 1

Answer:

$(\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} }) - (\frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} }) - (\frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } ) \\ = ( \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} } ) - (\frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} }) -( \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } ) \\ = \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3}) }{ {( \sqrt{10} )}^{2} - {( \sqrt{3} )}^{2} } - \frac{2 \sqrt{5} ( \sqrt{6} - \sqrt{5}) }{ {( \sqrt{6} )}^{2} - {( \sqrt{5} )}^{2} } - \frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} ) }{ {( \sqrt{15} )}^{2} - {(3 \sqrt{2} )}^{2} } \\ = \frac{7 \sqrt{30} - 21 }{10 - 3} - \frac{2 \sqrt{30} - 10}{6 - 5} - \frac{3 \sqrt{30} - 18}{15 - 18} \\ = \frac{7 \sqrt{30} - 21 }{7} - \frac{2 \sqrt{30} - 10}{1} - \frac{3 \sqrt{30} - 18}{ - 3} \\ = \frac{21 \sqrt{30 } - 63 - 42 \sqrt{30} - 210 + 21 \sqrt{30} - 126}{21} \\ = \frac{ - 399}{21} \\ = - 19 \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$