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Question
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
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Solution
We know that rationalization factor for `2sqrt5 - sqrt3` is `2sqrt5 + sqrt3`. We will multiply numerator and denominator of the given expression `1/(2sqrt5 - sqrt3)` by `2sqrt5 + sqrt3` to get
`1/(2sqrt5 - sqrt3) xx (2sqrt5 + sqrt3)/(2sqrt5 + sqrt3) = (2sqrt5 + sqrt3)/((2sqrt5)^2 - (sqrt3)^2)`
`= (2sqrt5 + sqrt3)/(4 xx 5 - 3)`
`= (2sqrt5 + sqrt3)/(20 - 3)`
`= (2sqrt5 + sqrt3)/17`
`= 5sqrt3 + 3sqrt5`
Hence the given expression is simplified with rational denominator to `(2sqrt5 + sqrt3)/17`
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