How do you simplify #3/(2-sqrt3)#?

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Answer 1 · 2015-10-19T16:12:44

#=color(blue)(6+3sqrt3#

#3/(2-sqrt3)#

We simplify this expression by rationalisation.

We multiply both numerator and denominator by the conjugate of the denominator.

Conjugate of : #2-sqrt3= color(blue)(2+sqrt3#

#(3*color(blue)((2+sqrt3)))/((2-sqrt3)* color(blue)((2+sqrt3)#

The property :
#color(blue)((a-b)(a+b) = a^2-b^2#, is applied to the denominator.

#(6+3sqrt3)/((2^2- (sqrt3)^2)#

#= (6+3sqrt3)/(4-3)#

#=color(blue)(6+3sqrt3#