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प्रश्न
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
उत्तर
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
Rationalizing the denominator of each term, we have
= `(6(2sqrt(3) + sqrt(6)))/((2sqrt(3) - sqrt(6))(2sqrt(3) + sqrt(6))) + (sqrt(6)(sqrt(3) - sqrt(2)))/((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))) - (4sqrt(3)(sqrt(6) + sqrt(2)))/((sqrt(6) - sqrt(2))(sqrt(6) + sqrt(2))`
= `(12sqrt(3) + 6sqrt(6))/(12 - 6) + (sqrt(18) - sqrt(12))/(3 - 2) - (4sqrt(18) + 4sqrt(6))/(6 - 2)`
= `(12sqrt(3) + 6sqrt(6))/(6) + (sqrt(18) - sqrt(12))/(1) - (4sqrt(18) + 4sqrt(6))/(4)`
= `2sqrt(3) + sqrt(6) + sqrt(18) - sqrt(12) - sqrt(18) - sqrt(6)`
= `2sqrt(3) - sqrt(12)`
= `2sqrt(3) - 2sqrt(3)`
= 0
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