How do you simplify #(2 -sqrt 5) /(3 +sqrt5)#?

2 Answers
Jun 20, 2018

Answer:

#color(chocolate)(=> 11/4 - (5sqrt5)/4#

Explanation:

#(2 - sqrt5) / (3 + sqrt5)#

#=> ((2 - sqrt5) * (3 - sqrt5)) / ((3 + sqrt5) (3 - sqrt5))#

#=> (6 - 2 sqrt5 -3sqrt5 + 5 ) / (9 - 5)#

#=> (11 - 5sqrt5) / 4#

#color(chocolate)(=> 11/4 - (5sqrt5)/4#

Jun 20, 2018

Answer:

#11/4-(5sqrt5)/4#

Explanation:

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

#"the conjugate of "3+sqrt5" is "3color(red)(-)sqrt5#

#=((2-sqrt5)(3-sqrt5))/((3+sqrt5)(3-sqrt5))#

#"expand factors on numerator/denominator"#

#=(6-5sqrt5+5)/(9-5)#

#=(11-5sqrt5)/4=11/4-(5sqrt5)/4#