# How do you rationalize the denominator and simplify 5/(sqrt[3] + sqrt[5])?

##### 1 Answer
Oct 5, 2015

=color(blue)((-5(sqrt3-sqrt5))/2

#### Explanation:

Rationalizing involves multiplying the numerator and the denominator of the expression by the conjugate of the denominator.

The conjugate of the denominator is
sqrt3+sqrt5 = color(blue)(sqrt3-sqrt5

Rationalizing

5/(sqrt3+sqrt5)= (5* color(blue)((sqrt3-sqrt5)))/((sqrt3+sqrt5)* color(blue)((sqrt3-sqrt5))

The denominator can be simplified by applying the property
$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

So,
(sqrt3+sqrt5)* (sqrt3-sqrt5)=3-5=color(blue)(-2

The expression then becomes:

(5sqrt3-5sqrt5)/color(blue)(-2

=color(blue)((5(sqrt3-sqrt5))/-2