Question
Answer
$$\dfrac{-6}{10+\sqrt{15}}=\dfrac{-60+6\sqrt{15}}{85}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-6}{10+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-6}{10+\sqrt{15}}\frac{10-\sqrt{15}}{10-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-60+6\sqrt{15}}{100-10\sqrt{15}+10\sqrt{15}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-60+6\sqrt{15}}{85}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 10- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -6 } \cdot \left( 10- \sqrt{15}\right) = \color{blue}{-6} \cdot10\color{blue}{-6} \cdot- \sqrt{15} = \\ = -60 + 6 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( 10 + \sqrt{15}\right) } \cdot \left( 10- \sqrt{15}\right) = \color{blue}{10} \cdot10+\color{blue}{10} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot10+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 100- 10 \sqrt{15} + 10 \sqrt{15}-15 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator