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Question
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
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Solution
We know that rationalization factor for `2sqrt2 - sqrt3` is `2sqrt2 + sqrt3` . We will multiply numerator and denominator of the given expression `(sqrt3 + 1)/(2sqrt2 - sqrt3)` by `2sqrt2 + sqrt3` to get
`(sqrt3 + 1)/(2sqrt2 - sqrt3) xx (2sqrt2 + sqrt3)/(2sqrt2 + sqrt3) = (2xx sqrt3 xx sqrt2 + sqrt3 xx sqrt3 + 2sqrt2 + sqrt3)/((2sqrt2)^2 - (sqrt3)^2)`
` = (2sqrt(3xx2) + 3 + 2 sqrt2 + sqrt3)/(4 xx 2 - 3)`
`= (2sqrt6 + 3 + 2sqrt2 + sqrt3)/(8 - 3)`
`= (2sqrt6 + 3 + 2sqrt2 + sqrt3)/5`
`= (2sqrt6 + 3 + 2sqrt2 + sqrt3)/5`
Hence the given expression is simplified with rational denominator to `(2sqrt6 + 3 + 2sqrt2 + sqrt3)/5`
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