Answer
$$\frac{63}{2\sqrt{462}-20}=\frac{126\sqrt{462}+1260}{1448}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{63}{2\sqrt{462}-20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{63}{2\sqrt{462}-20}\frac{2\sqrt{462}+20}{2\sqrt{462}+20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{126\sqrt{462}+1260}{1848+40\sqrt{462}-40\sqrt{462}-400} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{126\sqrt{462}+1260}{1448}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{462} + 20} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 63 } \cdot \left( 2 \sqrt{462} + 20\right) = \color{blue}{63} \cdot 2 \sqrt{462}+\color{blue}{63} \cdot20 = \\ = 126 \sqrt{462} + 1260 $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{462}-20\right) } \cdot \left( 2 \sqrt{462} + 20\right) = \color{blue}{ 2 \sqrt{462}} \cdot 2 \sqrt{462}+\color{blue}{ 2 \sqrt{462}} \cdot20\color{blue}{-20} \cdot 2 \sqrt{462}\color{blue}{-20} \cdot20 = \\ = 1848 + 40 \sqrt{462}- 40 \sqrt{462}-400 $$ |
| ③ | Simplify numerator and denominator |
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