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

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Answer 1 · 2016-07-30T06:43:05

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

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))#