# How do you rationalize the denominator and simplify #(3-sqrt5)/(4+sqrt5)#?

##### 1 Answer

Mar 17, 2016

#### Explanation:

#(3-sqrt(5))/(4+sqrt(5))#

#=(3-sqrt(5))/(4+sqrt(5))((4-sqrt(5))/(4-sqrt(5)))#

#=(12-3sqrt(5)-4sqrt(5)+5)/(4+sqrt(5))(1/(4-sqrt(5)))#

#=(17-7sqrt(5))/(4+sqrt(5))(1/(4-sqrt(5)))#

#=(17-7sqrt(5))/(16-5)#

#=color(green)(|bar(ul(color(white)(a/a)(17-7sqrt(5))/(11)color(white)(a/a)|)))#