Answer
$$\frac{4}{1+\sqrt{6}}=\frac{-4+4\sqrt{6}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{1+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{1+\sqrt{6}}\frac{1-\sqrt{6}}{1-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4-4\sqrt{6}}{1-\sqrt{6}+\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4-4\sqrt{6}}{-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-4+4\sqrt{6}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 1- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 } \cdot \left( 1- \sqrt{6}\right) = \color{blue}{4} \cdot1+\color{blue}{4} \cdot- \sqrt{6} = \\ = 4- 4 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 1 + \sqrt{6}\right) } \cdot \left( 1- \sqrt{6}\right) = \color{blue}{1} \cdot1+\color{blue}{1} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot1+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 1- \sqrt{6} + \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator