Question
Answer
$$\dfrac{3}{6-5\sqrt{10}}=-\dfrac{18+15\sqrt{10}}{214}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{6-5\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{6-5\sqrt{10}}\frac{6+5\sqrt{10}}{6+5\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18+15\sqrt{10}}{36+30\sqrt{10}-30\sqrt{10}-250} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{18+15\sqrt{10}}{-214} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{18+15\sqrt{10}}{214}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6 + 5 \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( 6 + 5 \sqrt{10}\right) = \color{blue}{3} \cdot6+\color{blue}{3} \cdot 5 \sqrt{10} = \\ = 18 + 15 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( 6- 5 \sqrt{10}\right) } \cdot \left( 6 + 5 \sqrt{10}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot 5 \sqrt{10}\color{blue}{- 5 \sqrt{10}} \cdot6\color{blue}{- 5 \sqrt{10}} \cdot 5 \sqrt{10} = \\ = 36 + 30 \sqrt{10}- 30 \sqrt{10}-250 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
This page was created using
Rationalize Denominator Calculator