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:

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

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

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

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