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
$color(blue)(1-sqrt3)$

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

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

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

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

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

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