How do you simplify #(1+2sqrt3)/(1+sqrt3)#?

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Answer 1 · 2015-07-07T05:33:07

#=color(blue)(( 5-sqrt3)/(2)#

#(1+2sqrt3)/(1+sqrt3)#

Multiplying the numerator and denominator by the conjugate
#color(blue)(1-sqrt3)#

#=((1+2sqrt3) . (color(blue)(1-sqrt3)))/((1+sqrt3). color(blue)((1-sqrt3)))#

#=((1-sqrt3+2sqrt3-2sqrt3 .sqrt 3))/(1^2 - (sqrt3)^2)#

#=((1 + sqrt3 - 6))/(1 - 3)#

#=((sqrt3 - 5))/(-2)#

#=color(blue)((( 5-sqrt3))/(2)#