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

Oct 19, 2015

=color(blue)(6+3sqrt3

#### Explanation:

$\frac{3}{2 - \sqrt{3}}$

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)

$= \frac{6 + 3 \sqrt{3}}{4 - 3}$

=color(blue)(6+3sqrt3