Answer
$$\frac{3}{\sqrt{17}-4}=3\sqrt{17}+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{\sqrt{17}-4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{\sqrt{17}-4}\frac{\sqrt{17}+4}{\sqrt{17}+4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{17}+12}{17+4\sqrt{17}-4\sqrt{17}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{17}+12}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3\sqrt{17}+12\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{17} + 4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( \sqrt{17} + 4\right) = \color{blue}{3} \cdot \sqrt{17}+\color{blue}{3} \cdot4 = \\ = 3 \sqrt{17} + 12 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{17}-4\right) } \cdot \left( \sqrt{17} + 4\right) = \color{blue}{ \sqrt{17}} \cdot \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot4\color{blue}{-4} \cdot \sqrt{17}\color{blue}{-4} \cdot4 = \\ = 17 + 4 \sqrt{17}- 4 \sqrt{17}-16 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Remove 1 from denominator. |
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