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

1 Answer
Jul 30, 2016

-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))