(-√3+1)/(√3+1) how to simplify?

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Answer 1 · 2018-07-14T04:01:06

#sqrt(3) - 2#

Given: #(-sqrt(3) + 1)/(sqrt(3) + 1)#

Multiply by the conjugate of the denominator as 1: #sqrt(3) - 1# to eliminate the radical in the denominator:

#(-sqrt(3) + 1)/(sqrt(3) + 1) * (sqrt(3) - 1)/(sqrt(3) - 1) = (-3 + sqrt(3) + sqrt(3) - 1)/(3 - 1) = (2 sqrt(3) - 4)/2#

#= (cancel(2)(sqrt(3) - 2))/cancel(2) = sqrt(3) - 2#

Answer 2 · 2018-07-14T13:21:51

#sqrt3-2#

#(-sqrt3+1)/(sqrt3+1)#

=#-(sqrt3-1)/(sqrt3+1)#

=#-(sqrt3-1)^2/((sqrt3)^2-1^2)#

=#-(4-2sqrt3)/(3-1)#

=#-(4-2sqrt3)/2#

=#-(2-sqrt3)#

=#sqrt3-2#