Answer
$$\frac{2+\sqrt{5}}{3+\sqrt{4}}=\frac{2+\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2+\sqrt{5}}{3+\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2+\sqrt{5}}{3+\sqrt{4}}\frac{3-\sqrt{4}}{3-\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6-4+3\sqrt{5}-2\sqrt{5}}{9-6+6-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2+\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3- \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 2 + \sqrt{5}\right) } \cdot \left( 3- \sqrt{4}\right) = \color{blue}{2} \cdot3+\color{blue}{2} \cdot- \sqrt{4}+\color{blue}{ \sqrt{5}} \cdot3+\color{blue}{ \sqrt{5}} \cdot- \sqrt{4} = \\ = 6-4 + 3 \sqrt{5}- 2 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( 3 + \sqrt{4}\right) } \cdot \left( 3- \sqrt{4}\right) = \color{blue}{3} \cdot3+\color{blue}{3} \cdot- \sqrt{4}+\color{blue}{ \sqrt{4}} \cdot3+\color{blue}{ \sqrt{4}} \cdot- \sqrt{4} = \\ = 9-6 + 6-4 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator