Answer
$$\frac{\frac{\sqrt{13}}{4}}{\frac{\sqrt{3}}{4}}=\frac{\sqrt{39}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\sqrt{13}}{4}}{\frac{\sqrt{3}}{4}}& \xlongequal{ }\frac{\sqrt{13}}{4}\cdot\frac{4}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{13}}{4\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{13}}{4\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{39}}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{39}}{3}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \sqrt{13} } \cdot 4 = 4 \sqrt{13} $$$$ \color{blue}{ 4 } \cdot \sqrt{3} = 4 \sqrt{3} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{13} } \cdot \sqrt{3} = 4 \sqrt{39} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{3} } \cdot \sqrt{3} = 12 $$ |
| ④ | Divide both numerator and denominator by 4. |
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