Answer
$$\frac{2\sqrt{5}+3\sqrt{5}}{2\sqrt{5}-3\sqrt{5}}=-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{5}+3\sqrt{5}}{2\sqrt{5}-3\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{5}}{-\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{5}}{-\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{25}{-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{25}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}- \, \frac{ 25 : \color{orangered}{ 5 } }{ 5 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{5}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-5\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{5} } \cdot \sqrt{5} = 25 $$ Simplify denominator. $$ \color{blue}{ - \sqrt{5} } \cdot \sqrt{5} = -5 $$ |
| ④ | Place minus sign in front of the fraction. |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $. |
| ⑥ | Remove 1 from denominator. |
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