How do you simplify #(2-sqrt3)/(-2-sqrt5)#?

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Answer 1 · 2017-07-09T12:45:04

See a solution process below:

First, we will rationalize the denominator to remove the radicals from the denominator by multiplying the expression by the necessary form or #1#:

#(-2 + sqrt(5))/(-2 + sqrt(5)) xx (2 - sqrt(3))/(-2 - sqrt(5)) =>#

#((-2 * 2) + 2sqrt(3) + 2sqrt(5) - sqrt(5)sqrt(3))/((-2 * -2) + 2sqrt(5) - 2sqrt(5) - sqrt(5)sqrt(5)) =>#

#(-4 + 2sqrt(3) + 2sqrt(5) - sqrt(15))/(4 + 0 - 5) =>#

#(-4 + 2sqrt(3) + 2sqrt(5) - sqrt(15))/-1 =>#

#4 - 2sqrt(3) - 2sqrt(5) + sqrt(15)#

Or

#4 - 2(sqrt(3) + sqrt(5)) + sqrt(15)#