Question
Answer
$$\dfrac{2\sqrt{6}-5}{2\sqrt{6}+5}=-49+20\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{6}-5}{2\sqrt{6}+5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{6}-5}{2\sqrt{6}+5}\frac{2\sqrt{6}-5}{2\sqrt{6}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24-10\sqrt{6}-10\sqrt{6}+25}{24-10\sqrt{6}+10\sqrt{6}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{49-20\sqrt{6}}{-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-49+20\sqrt{6}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-49+20\sqrt{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{6}-5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 2 \sqrt{6}-5\right) } \cdot \left( 2 \sqrt{6}-5\right) = \color{blue}{ 2 \sqrt{6}} \cdot 2 \sqrt{6}+\color{blue}{ 2 \sqrt{6}} \cdot-5\color{blue}{-5} \cdot 2 \sqrt{6}\color{blue}{-5} \cdot-5 = \\ = 24- 10 \sqrt{6}- 10 \sqrt{6} + 25 $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{6} + 5\right) } \cdot \left( 2 \sqrt{6}-5\right) = \color{blue}{ 2 \sqrt{6}} \cdot 2 \sqrt{6}+\color{blue}{ 2 \sqrt{6}} \cdot-5+\color{blue}{5} \cdot 2 \sqrt{6}+\color{blue}{5} \cdot-5 = \\ = 24- 10 \sqrt{6} + 10 \sqrt{6}-25 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
| ⑤ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator