How do you rationalize the denominator and simplify #(3sqrt5 )/( 4sqrt3 - 5sqrt2)#?

1 Answer
Jul 30, 2016

Answer:

#-3/2sqrt(5)(4sqrt(3)+5sqrt(2))#

Explanation:

Since

#(a+b)(a-b)=a^2-b^2#,

you can multiply numerator and denominator of the fraction by the same expression

#(4sqrt(3)+5sqrt(2))#

to have:

#(3sqrt(5)(4sqrt(3)+5sqrt(2)))/((4sqrt(3)-5sqrt(2))(4sqrt(3)+5sqrt(2)))=#

#(3sqrt(5)(4sqrt(3)+5sqrt(2)))/(48-50)=#

#-3/2sqrt(5)(4sqrt(3)+5sqrt(2))#