Rationalize denominator, all variables positive real numbers and denominator is not zero.
sqrt3/3 sqrt2 - sqrt3
sqrt3(3sqrt2+sqrt3)/18-3
3 sqrt6+3/18-3
3 sqrt 6+3/15 (is this my answer)
yes, but you must have brackets in your solutions
i.e.
(3 sqrt 6+3)/15 or (3√6 + 3)/15
To rationalize the denominator, you have to eliminate any square roots from the denominator. In this case, the denominator is 3 √2 - √3.
To do that, you can multiply both the numerator and denominator by the conjugate of the denominator, which is 3 √2 + √3.
(sqrt3/3 √2 - sqrt3) * (3 √2 + √3)/(3 √2 + √3)
Now, let's simplify the numerator and denominator separately:
Numerator:
(sqrt3) * (3 √2 + √3) = 3 √6 + √9 = 3 √6 + 3
Denominator:
(3 √2 - √3) * (3 √2 + √3) = (3 √2)^2 - (√3)^2 = 9 * 2 - 3 = 18 - 3 = 15
Therefore, the rationalized form of the fraction is (3 √6 + 3)/15.
So, your answer is correct: 3 √6 + 3/15.