Question
Answer
$$\dfrac{10}{-\sqrt{21}+\sqrt{35}}=\dfrac{10\sqrt{21}+10\sqrt{35}}{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10}{-\sqrt{21}+\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10}{-\sqrt{21}+\sqrt{35}}\frac{-\sqrt{21}-\sqrt{35}}{-\sqrt{21}-\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-10\sqrt{21}-10\sqrt{35}}{21+7\sqrt{15}-7\sqrt{15}-35} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-10\sqrt{21}-10\sqrt{35}}{-14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{10\sqrt{21}+10\sqrt{35}}{14}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ - \sqrt{21}- \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 } \cdot \left( - \sqrt{21}- \sqrt{35}\right) = \color{blue}{10} \cdot- \sqrt{21}+\color{blue}{10} \cdot- \sqrt{35} = \\ = - 10 \sqrt{21}- 10 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ \left( - \sqrt{21} + \sqrt{35}\right) } \cdot \left( - \sqrt{21}- \sqrt{35}\right) = \color{blue}{- \sqrt{21}} \cdot- \sqrt{21}\color{blue}{- \sqrt{21}} \cdot- \sqrt{35}+\color{blue}{ \sqrt{35}} \cdot- \sqrt{21}+\color{blue}{ \sqrt{35}} \cdot- \sqrt{35} = \\ = 21 + 7 \sqrt{15}- 7 \sqrt{15}-35 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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