Answer
$$\frac{4+\sqrt{2}}{3\sqrt{2}}=\frac{2\sqrt{2}+1}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4+\sqrt{2}}{3\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4+\sqrt{2}}{3\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{2}+2}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{2}+1}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4 + \sqrt{2}\right) } \cdot \sqrt{2} = \color{blue}{4} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot \sqrt{2} = \\ = 4 \sqrt{2} + 2 $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{2} } \cdot \sqrt{2} = 6 $$ |
| ③ | Divide both numerator and denominator by 2. |
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