Question

Which of the following is equivalent to the radical expression below, when the denominator has been rationalized and X >_ 6?

Answer 1

the correct choice is marked

Explanation:

To rationalize the denominator, you multiply both numerator and denominator by the sum of the terms whose difference is the current denominator.

`(12)/(√(x)-√(x-6))=(12(√(x)+√(x-6)))/((√(x)-√(x-6))(√(x)+√(x-6)))=(12(√(x)+√(x-6)))/((√(x))^2-(√(x-6))^2)\\\\=(12(√(x)+√(x-6)))/(x-(x-6))=(12(√(x)+√(x-6)))/(6)\\\\=\boxed{2(√(x)+√(x-6))}`