Question

Which of the following is equivalent to the fraction below when the denominator has been rationalized and

Answer 1

Rationalizing the denominator,

`\begin{gathered} (12)/(√(x)-√(x-6))*(√(x)+√(x-6))/(√(x)+√(x-6))=(12(√(x)+√(x-6)))/((√(x)-√(x-6))(√(x)+√(x-6))) \\ \\ =(12(√(x)+√(x-6)))/(x-(x-6))=(12(√(x)+√(x-6)))/(x-x+6)=(12(√(x)+√(x-6)))/(6)=2(√(x)+√(x-6)) \end{gathered}`

The correct option is C.