Given: A fraction
[tex]\frac{2-\sqrt{2}}{2+\sqrt{2}}[/tex]
Required: To simplify the given fraction.
Explanation: The given fraction can be simplified by rationalizing the denominator of the fraction. The rationalizing factor is
[tex]2-\sqrt{2}[/tex]
Hence,
[tex]\begin{gathered} \frac{(2-\sqrt{2})}{2+\sqrt{2}}\times\frac{(2-\sqrt{2})}{(2-\sqrt{2})} \\ \frac{(2-\sqrt{2})^2}{(2)^2-(\sqrt{2}^{)2}} \end{gathered}[/tex]
Which gives
[tex]\begin{gathered} \frac{4+2-4\sqrt{2}}{4-2} \\ \frac{2(3-2\sqrt{2})}{2} \\ 3-2\sqrt{2} \end{gathered}[/tex]
Final Answer: Option A is correct.
