Answer
$$\frac{5}{-6+\sqrt{6}}=\frac{-6-\sqrt{6}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{-6+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{-6+\sqrt{6}}\frac{-6-\sqrt{6}}{-6-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-30-5\sqrt{6}}{36+6\sqrt{6}-6\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-30-5\sqrt{6}}{30} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-6-\sqrt{6}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -6- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( -6- \sqrt{6}\right) = \color{blue}{5} \cdot-6+\color{blue}{5} \cdot- \sqrt{6} = \\ = -30- 5 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( -6 + \sqrt{6}\right) } \cdot \left( -6- \sqrt{6}\right) = \color{blue}{-6} \cdot-6\color{blue}{-6} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot-6+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 36 + 6 \sqrt{6}- 6 \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 5. |
This page was created using
Rationalize Denominator Calculator