# How do you rationalize the denominator and simplify #2/(1-sqrt5)#?

##### 2 Answers

Apr 28, 2018

#### Explanation:

To do this we must multiply both numerator and denominator by the denominators conjugate:

As this is just the same as multiplying by 1:

Expanding:

Apr 28, 2018

#### Explanation:

#"to "color(blue)"rationalise the denominator"#

#"multiply the numerator/denominator by the "color(blue)"conjugate"#

#"of the denominator"#

#"the conjugate of "1-sqrt5" is "1color(red)(+)sqrt5#

#rArr(2(1+sqrt5))/((1-sqrt5)(1+sqrt5))#

#"expand the denominator using FOIL"#

#(2(1+sqrt5))/(-4)=-1/2(1+sqrt5)#