Question

Which choice is equivalent to the fraction below when x> 2

Answer 1

The expression is given below as

`(4)/(√(x-2)-√(x))`

Concept:

To rationalize the denominator, we will multiply by the conjugate given below

The conjugate is given below as

`(√(x-2)+√(x))/(√(x-2)+√(x))`

Step 1:

Multiply the expression in the question by the conjugate, we will have

`(4)/(√(x-2)-√(x))*(√(x-2)+√(x))/(√(x-2)+√(x))`

By expanding the brackets, we will have

`\begin{gathered} \frac{4√(x-2)+4√(x)}{(\sqrt{x-2)^2-(√(x))^2}} \\ =(4√(x-2)+4√(x))/(x-2-x) \\ =(4√(x-2)+4√(x))/(-2) \end{gathered}`

Step 2:

Factor our the common number and divide

`\begin{gathered} =(4(√(x-2)+√(x)))/(-2) \\ =-2(√(x)+√(x-2)) \end{gathered}`

Hence,

The final answer is

`\Rightarrow-2(√(x)+√(x-2))`

OPTION A is the right answer