Answer
$$\frac{\sqrt{17}-\sqrt{11}}{\sqrt{17}+\sqrt{11}}=\frac{14-\sqrt{187}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{17}-\sqrt{11}}{\sqrt{17}+\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{17}-\sqrt{11}}{\sqrt{17}+\sqrt{11}}\frac{\sqrt{17}-\sqrt{11}}{\sqrt{17}-\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{17-\sqrt{187}-\sqrt{187}+11}{17-\sqrt{187}+\sqrt{187}-11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28-2\sqrt{187}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{14-\sqrt{187}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{17}- \sqrt{11}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{17}- \sqrt{11}\right) } \cdot \left( \sqrt{17}- \sqrt{11}\right) = \color{blue}{ \sqrt{17}} \cdot \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot- \sqrt{11}\color{blue}{- \sqrt{11}} \cdot \sqrt{17}\color{blue}{- \sqrt{11}} \cdot- \sqrt{11} = \\ = 17- \sqrt{187}- \sqrt{187} + 11 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{17} + \sqrt{11}\right) } \cdot \left( \sqrt{17}- \sqrt{11}\right) = \color{blue}{ \sqrt{17}} \cdot \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot- \sqrt{11}+\color{blue}{ \sqrt{11}} \cdot \sqrt{17}+\color{blue}{ \sqrt{11}} \cdot- \sqrt{11} = \\ = 17- \sqrt{187} + \sqrt{187}-11 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator