# How do you rationalize the denominator and simplify 5/(sqrt3-1)?

Apr 15, 2016

$= \frac{5 \sqrt{3} + 5}{2}$

#### Explanation:

$\frac{5}{\sqrt{3} - 1}$

To rationalize the expression, we multiply it by the conjugate of the denominator $\textcolor{b l u e}{\left(\sqrt{3} + 1\right)}$

(5 * color(blue)((sqrt 3 + 1 ) ))/ ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))

 =((5 * color(blue)((sqrt 3)) + 5 * color(blue)(( 1 )) ))/ ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))

 =(5sqrt 3 + 5 ) / ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))

• Applying property
color(blue)((a-b)(a+b) = a ^2 - b^2 to the denominator we get:

$= \frac{5 \sqrt{3} + 5}{{\left(\sqrt{3}\right)}^{2} - {1}^{2}}$

$= \frac{5 \sqrt{3} + 5}{3 - 1}$

$= \frac{5 \sqrt{3} + 5}{2}$