Question
Answer
$$\dfrac{5}{-4+\sqrt{10}}=\dfrac{-20-5\sqrt{10}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{-4+\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{-4+\sqrt{10}}\frac{-4-\sqrt{10}}{-4-\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-20-5\sqrt{10}}{16+4\sqrt{10}-4\sqrt{10}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-20-5\sqrt{10}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -4- \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( -4- \sqrt{10}\right) = \color{blue}{5} \cdot-4+\color{blue}{5} \cdot- \sqrt{10} = \\ = -20- 5 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( -4 + \sqrt{10}\right) } \cdot \left( -4- \sqrt{10}\right) = \color{blue}{-4} \cdot-4\color{blue}{-4} \cdot- \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot-4+\color{blue}{ \sqrt{10}} \cdot- \sqrt{10} = \\ = 16 + 4 \sqrt{10}- 4 \sqrt{10}-10 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator