[tex] \begin{aligned} & \frac{ \sqrt{2} }{2 \sqrt{6} - \sqrt{7} } \\ \\ & = \frac{ \sqrt{2} }{2 \sqrt{6} - \sqrt{7} } \times \frac{2 \sqrt{6} + \sqrt{7} }{2 \sqrt{6} + \sqrt{7} } \\ \\ & = \frac{ \sqrt{2} (2 \sqrt{6} + \sqrt{7}) }{4 \times 6 + 2 \sqrt{6 \times 7} - 2 \sqrt{6 \times 7} - 7} \\ \\ & = \frac{2 \sqrt{12} + \sqrt{14} }{24 + 2 \sqrt{42} - 2 \sqrt{42} - 7} \\ \\ & = \frac{2 \sqrt{4 \times 3} + \sqrt{14} }{24+ 0 - 7} \\ \\ & = \frac{2 \times 2 \sqrt{3} + \sqrt{14} }{24 - 7} \\ \\& = \frac{4 \sqrt{3} + \sqrt{14} }{17} \end{aligned} [/tex]
#LearnWithPanda
[tex] \mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}[/tex]
[tex] \boxed{ \bf{ \: \frac{4 \sqrt{3} + \sqrt{14} }{17} \: }}[/tex]
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[tex] \mathbb{ \color{orange}{ \underbrace{PENYELESAIAN}}}[/tex]
[tex] \boxed{ \: \begin{aligned} \tt{ \frac{ \sqrt{2} }{2 \sqrt{6} - \sqrt{7} } } &= \tt{ \frac{ \sqrt{2} }{2 \sqrt{6} - \sqrt{7} } \times \frac{2 \sqrt{6} + \sqrt{7} }{2 \sqrt{6} + \sqrt{7} } } \\ &= \tt{ \frac{2 \sqrt{12} + \sqrt{14} }{ {(2 \sqrt{6} )}^{2} - {( \sqrt{7} )}^{2} } } \\ &= \tt{ \frac{2 \sqrt{4 \cdot3} + \sqrt{14} }{4 \cdot6 - 7} } \\ &= \tt{ \frac{2 \sqrt{ {2}^{2} \cdot3} + \sqrt{14} }{24 - 7} } \\ &= \tt{ \frac{2 \cdot2 \sqrt{3} + \sqrt{14} }{17} } \\ &= \red{ \boxed{ \bf{ \pink{ \frac{4 \sqrt{3} + \sqrt{14} }{17} }}}} \end{aligned} \: }[/tex]
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[tex] \mathbb{ \color{red}{ \underbrace{KESIMPULAN}}}[/tex]
Jadi, bentuk rasional dari [tex] \bf{ \frac{ \sqrt{2} }{2 \sqrt{6} - \sqrt{7} } } [/tex] adalah [tex] \bf{ \pink{ \frac{4 \sqrt{3} + \sqrt{14} }{17} }} [/tex]
[tex] \colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{} [/tex]
[answer.2.content]