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

1 Answer
Apr 3, 2017

Answer:

You multiply the both halves by #sqrt7-sqrt3# and use the special product #(A+B)(A-B)=A^2-B^2#

Explanation:

#=4/(sqrt7-sqrt3)xx(sqrt7-sqrt3)/(sqrt7-sqrt3)#

#=(4(sqrt7-sqrt3))/((sqrt7+sqrt3)(sqrt7-sqrt3))#

#=(4(sqrt7-sqrt3))/(sqrt7^2-sqrt3^2)=(4(sqrt7-sqrt3))/(7-3)=#

#=(cancel4(sqrt7-sqrt3))/cancel4=sqrt7-sqrt3#