Question
Answer
$$\dfrac{1672}{-193\sqrt{209}}=-\dfrac{8\sqrt{209}}{193}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1672}{-193\sqrt{209}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1672}{-193\sqrt{209}}\frac{\sqrt{209}}{\sqrt{209}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1672\sqrt{209}}{-40337} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-\frac{1672\sqrt{209}}{40337} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{ 1672 \sqrt{ 209 } : \color{blue}{ 209 } } { 40337 : \color{blue}{ 209 }} \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{8\sqrt{209}}{193}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{209}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 1672 } \cdot \sqrt{209} = 1672 \sqrt{209} $$ Simplify denominator. $$ \color{blue}{ - 193 \sqrt{209} } \cdot \sqrt{209} = -40337 $$ |
| ③ | Place a negative sign in front of a fraction. |
| ④ | Divide numerator and denominator by $ \color{blue}{ 209 } $. |
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