Question
Answer
$$\dfrac{7\sqrt{11}}{\sqrt{12}+14}=\dfrac{-14\sqrt{33}+98\sqrt{11}}{184}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{11}}{\sqrt{12}+14}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{11}}{\sqrt{12}+14}\frac{\sqrt{12}-14}{\sqrt{12}-14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14\sqrt{33}-98\sqrt{11}}{12-28\sqrt{3}+28\sqrt{3}-196} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{14\sqrt{33}-98\sqrt{11}}{-184} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-14\sqrt{33}+98\sqrt{11}}{184}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12}-14} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 \sqrt{11} } \cdot \left( \sqrt{12}-14\right) = \color{blue}{ 7 \sqrt{11}} \cdot \sqrt{12}+\color{blue}{ 7 \sqrt{11}} \cdot-14 = \\ = 14 \sqrt{33}- 98 \sqrt{11} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{12} + 14\right) } \cdot \left( \sqrt{12}-14\right) = \color{blue}{ \sqrt{12}} \cdot \sqrt{12}+\color{blue}{ \sqrt{12}} \cdot-14+\color{blue}{14} \cdot \sqrt{12}+\color{blue}{14} \cdot-14 = \\ = 12- 28 \sqrt{3} + 28 \sqrt{3}-196 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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