Question
Answer
$$\dfrac{3}{6\sqrt{5}+4}=\dfrac{18\sqrt{5}-12}{164}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{6\sqrt{5}+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{6\sqrt{5}+4}\frac{6\sqrt{5}-4}{6\sqrt{5}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18\sqrt{5}-12}{180-24\sqrt{5}+24\sqrt{5}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{18\sqrt{5}-12}{164}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6 \sqrt{5}-4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( 6 \sqrt{5}-4\right) = \color{blue}{3} \cdot 6 \sqrt{5}+\color{blue}{3} \cdot-4 = \\ = 18 \sqrt{5}-12 $$ Simplify denominator. $$ \color{blue}{ \left( 6 \sqrt{5} + 4\right) } \cdot \left( 6 \sqrt{5}-4\right) = \color{blue}{ 6 \sqrt{5}} \cdot 6 \sqrt{5}+\color{blue}{ 6 \sqrt{5}} \cdot-4+\color{blue}{4} \cdot 6 \sqrt{5}+\color{blue}{4} \cdot-4 = \\ = 180- 24 \sqrt{5} + 24 \sqrt{5}-16 $$ |
| ③ | Simplify numerator and denominator |
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