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Question
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
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Solution
`(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2)`
`=> (3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) xx (3sqrt2 - 2sqrt3)/(3sqrt2 - 2sqrt3) + (2sqrt3)/(sqrt3 - sqrt2) xx (sqrt3 + sqrt2)/(sqrt3 + sqrt2)`
`=> ((3sqrt2 - 2sqrt3)^2)/((3sqrt2)^2 - (2sqrt3)^2) + (2sqrt3 (sqrt3 + sqrt2))/((sqrt3)^2 - (sqrt2)^2)`
`=> ((3sqrt2)^2 + (2sqrt3)^2 - 2 xx 3sqrt2 xx 2sqrt3)/((9 xx 2) - (4 xx 3)) + (6 + 2sqrt6)/(3 - 2)`
`=> (18 + 12 - 12sqrt6)/(18 - 12) + 6 + 2sqrt6`
`=> (30 - 12sqrt6)/6 + 6 + 2sqrt6`
`=> (cancel(6) (5 - 2sqrt6))/cancel(6) + 6 + 2sqrt6`
`=> 5 - cancel(2sqrt6) + 6 + cancel(2sqrt6)`
= 5 + 6
= 11
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