How do you simplify #(4 - sqrt 7) /(3+sqrt7)#?

2 Answers
Jul 25, 2018

Answer:

#19/2-7/2sqrt7#

Explanation:

#"multiply the numerator/denominator by the conjugate of"#
#"the denominator"#

#"the conjugate of "3+sqrt7" is "3color(red)(-)sqrt7#

#=((4-sqrt7)(3-sqrt7))/((3+sqrt7)(3-sqrt7))#

#=(12-7sqrt7+7)/(9-7)#

#=(19-7sqrt7)/2=19/2-7/2sqrt7#

Answer:

#frac{19-7\sqrt7}{2}#

Explanation:

#\frac{4-\sqrt7}{3+\sqrt7}#

#=\frac{(4-\sqrt7)(3-\sqrt7)}{(3+\sqrt7)(3-\sqrt7)}#

#=\frac{12-3\sqrt7-4\sqrt7+7}{3^2-(\sqrt7)^2}#

#=\frac{19-7\sqrt7}{9-7}#

#=\frac{19-7\sqrt7}{2}#