Question
Answer
$$\dfrac{7}{-10+\sqrt{3}}=\dfrac{-70-7\sqrt{3}}{97}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7}{-10+\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7}{-10+\sqrt{3}}\frac{-10-\sqrt{3}}{-10-\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-70-7\sqrt{3}}{100+10\sqrt{3}-10\sqrt{3}-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-70-7\sqrt{3}}{97}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -10- \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 } \cdot \left( -10- \sqrt{3}\right) = \color{blue}{7} \cdot-10+\color{blue}{7} \cdot- \sqrt{3} = \\ = -70- 7 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( -10 + \sqrt{3}\right) } \cdot \left( -10- \sqrt{3}\right) = \color{blue}{-10} \cdot-10\color{blue}{-10} \cdot- \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot-10+\color{blue}{ \sqrt{3}} \cdot- \sqrt{3} = \\ = 100 + 10 \sqrt{3}- 10 \sqrt{3}-3 $$ |
| ③ | Simplify numerator and denominator |
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