Question
Answer
$$\dfrac{-5}{\sqrt{6}+\sqrt{15}}=\dfrac{5\sqrt{6}-5\sqrt{15}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-5}{\sqrt{6}+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-5}{\sqrt{6}+\sqrt{15}}\frac{\sqrt{6}-\sqrt{15}}{\sqrt{6}-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-5\sqrt{6}+5\sqrt{15}}{6-3\sqrt{10}+3\sqrt{10}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-5\sqrt{6}+5\sqrt{15}}{-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{6}-5\sqrt{15}}{9}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -5 } \cdot \left( \sqrt{6}- \sqrt{15}\right) = \color{blue}{-5} \cdot \sqrt{6}\color{blue}{-5} \cdot- \sqrt{15} = \\ = - 5 \sqrt{6} + 5 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + \sqrt{15}\right) } \cdot \left( \sqrt{6}- \sqrt{15}\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot \sqrt{6}+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 6- 3 \sqrt{10} + 3 \sqrt{10}-15 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator