Question

Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator and simplify.)A.B.C.2D.

Answer 1

Given: A fraction

`(2-√(2))/(2+√(2))`

Required: To simplify the given fraction.

Explanation: The given fraction can be simplified by rationalizing the denominator of the fraction. The rationalizing factor is

`2-√(2)`

Hence,

`\begin{gathered} ((2-√(2)))/(2+√(2))*((2-√(2)))/((2-√(2))) \\ ((2-√(2))^2)/((2)^2-(√(2)^()2)) \end{gathered}`

Which gives

`\begin{gathered} (4+2-4√(2))/(4-2) \\ (2(3-2√(2)))/(2) \\ 3-2√(2) \end{gathered}`

Final Answer: Option A is correct.