Verified answer

Rationalize the numerator

(6 * (a + h) - 6a) / (h * (sqrt(6 * (a + h)) + sqrt(6a))) =>

(6a + 6h - 6a) / (h * (sqrt(6 * (a + h)) + sqrt(6a))) =>

6 / (sqrt(6 * (a + h)) + sqrt(6a))

h goes to 0

6 / (sqrt(6a) + sqrt(6a)) =>

6 / (2sqrt(6a)) =>

3 / sqrt(6a) =>

3 * sqrt(6a) / (6a) =>

sqrt(6a) / (2a)