Answer
$$\frac{-3}{\sqrt{3}-\sqrt{6}}=\sqrt{3}+\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-3}{\sqrt{3}-\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-3}{\sqrt{3}-\sqrt{6}}\frac{\sqrt{3}+\sqrt{6}}{\sqrt{3}+\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-3\sqrt{3}-3\sqrt{6}}{3+3\sqrt{2}-3\sqrt{2}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-3\sqrt{3}-3\sqrt{6}}{-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-\sqrt{3}-\sqrt{6}}{-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{\sqrt{3}+\sqrt{6}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\sqrt{3}+\sqrt{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3} + \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -3 } \cdot \left( \sqrt{3} + \sqrt{6}\right) = \color{blue}{-3} \cdot \sqrt{3}\color{blue}{-3} \cdot \sqrt{6} = \\ = - 3 \sqrt{3}- 3 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{3}- \sqrt{6}\right) } \cdot \left( \sqrt{3} + \sqrt{6}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot \sqrt{6}\color{blue}{- \sqrt{6}} \cdot \sqrt{3}\color{blue}{- \sqrt{6}} \cdot \sqrt{6} = \\ = 3 + 3 \sqrt{2}- 3 \sqrt{2}-6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 3. |
| ⑤ | Multiply both numerator and denominator by -1. |
| ⑥ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator