Question
Answer
$$\dfrac{7}{\sqrt{10}+4}=\dfrac{-7\sqrt{10}+28}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7}{\sqrt{10}+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7}{\sqrt{10}+4}\frac{\sqrt{10}-4}{\sqrt{10}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{10}-28}{10-4\sqrt{10}+4\sqrt{10}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7\sqrt{10}-28}{-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-7\sqrt{10}+28}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}-4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 } \cdot \left( \sqrt{10}-4\right) = \color{blue}{7} \cdot \sqrt{10}+\color{blue}{7} \cdot-4 = \\ = 7 \sqrt{10}-28 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{10} + 4\right) } \cdot \left( \sqrt{10}-4\right) = \color{blue}{ \sqrt{10}} \cdot \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot-4+\color{blue}{4} \cdot \sqrt{10}+\color{blue}{4} \cdot-4 = \\ = 10- 4 \sqrt{10} + 4 \sqrt{10}-16 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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