Question
Answer
$$\dfrac{7}{7\sqrt{6}+5}=\dfrac{49\sqrt{6}-35}{269}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7}{7\sqrt{6}+5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7}{7\sqrt{6}+5}\frac{7\sqrt{6}-5}{7\sqrt{6}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{49\sqrt{6}-35}{294-35\sqrt{6}+35\sqrt{6}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{49\sqrt{6}-35}{269}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 7 \sqrt{6}-5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 } \cdot \left( 7 \sqrt{6}-5\right) = \color{blue}{7} \cdot 7 \sqrt{6}+\color{blue}{7} \cdot-5 = \\ = 49 \sqrt{6}-35 $$ Simplify denominator. $$ \color{blue}{ \left( 7 \sqrt{6} + 5\right) } \cdot \left( 7 \sqrt{6}-5\right) = \color{blue}{ 7 \sqrt{6}} \cdot 7 \sqrt{6}+\color{blue}{ 7 \sqrt{6}} \cdot-5+\color{blue}{5} \cdot 7 \sqrt{6}+\color{blue}{5} \cdot-5 = \\ = 294- 35 \sqrt{6} + 35 \sqrt{6}-25 $$ |
| ③ | Simplify numerator and denominator |
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