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