Question
Answer
$$\dfrac{4}{\sqrt{3}-\sqrt{10}}=-\dfrac{4\sqrt{3}+4\sqrt{10}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{\sqrt{3}-\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{\sqrt{3}-\sqrt{10}}\frac{\sqrt{3}+\sqrt{10}}{\sqrt{3}+\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{3}+4\sqrt{10}}{3+\sqrt{30}-\sqrt{30}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{3}+4\sqrt{10}}{-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{4\sqrt{3}+4\sqrt{10}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3} + \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 } \cdot \left( \sqrt{3} + \sqrt{10}\right) = \color{blue}{4} \cdot \sqrt{3}+\color{blue}{4} \cdot \sqrt{10} = \\ = 4 \sqrt{3} + 4 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{3}- \sqrt{10}\right) } \cdot \left( \sqrt{3} + \sqrt{10}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot \sqrt{10}\color{blue}{- \sqrt{10}} \cdot \sqrt{3}\color{blue}{- \sqrt{10}} \cdot \sqrt{10} = \\ = 3 + \sqrt{30}- \sqrt{30}-10 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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