Answer
$$\frac{3}{2+\sqrt{17}}=\frac{-6+3\sqrt{17}}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{2+\sqrt{17}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{2+\sqrt{17}}\frac{2-\sqrt{17}}{2-\sqrt{17}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6-3\sqrt{17}}{4-2\sqrt{17}+2\sqrt{17}-17} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6-3\sqrt{17}}{-13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-6+3\sqrt{17}}{13}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2- \sqrt{17}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( 2- \sqrt{17}\right) = \color{blue}{3} \cdot2+\color{blue}{3} \cdot- \sqrt{17} = \\ = 6- 3 \sqrt{17} $$ Simplify denominator. $$ \color{blue}{ \left( 2 + \sqrt{17}\right) } \cdot \left( 2- \sqrt{17}\right) = \color{blue}{2} \cdot2+\color{blue}{2} \cdot- \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot2+\color{blue}{ \sqrt{17}} \cdot- \sqrt{17} = \\ = 4- 2 \sqrt{17} + 2 \sqrt{17}-17 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator