18 / ( sqrt5 - 3 sqrt5 )
Rationalizing the expression , by multiplying it with the conjugate of the denominator : color(blue)(sqrt5 + 3 sqrt5
(18 * (color(blue)(sqrt5 + 3 sqrt5) ))/ (( sqrt5 - 3 sqrt5 ) * color(blue)((sqrt5 + 3 sqrt5))
= (18 * (color(blue)(sqrt5)) + 18 * color(blue)((3 sqrt5)) )/ (( sqrt5 - 3 sqrt5 ) * color(blue)((sqrt5 + 3 sqrt5))
- Applying property color(blue)((a-b)(a+b) = a ^2 - b^2 to the denominator.
= (18sqrt5 + 54sqrt5)/ (sqrt(5^2 )- (3 sqrt5 )^2 )
= (18sqrt5 + 54sqrt5)/ (5 - (9 * 5) )
= (18sqrt5 + 54sqrt5)/ (5 - 45)
= (18sqrt5 + 54sqrt5)/ (- 40)
= (sqrt5(18 + 54))/ (- 40)
= (sqrt5(72))/ (- 40)
= (sqrt5(cancel72))/ (- cancel40)
= (sqrt5(9))/ (- 5)
= (- 9 sqrt5)/ 5
