Question
Answer
$$\dfrac{45}{2\sqrt{17}+5}=\dfrac{90\sqrt{17}-225}{43}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{45}{2\sqrt{17}+5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{45}{2\sqrt{17}+5}\frac{2\sqrt{17}-5}{2\sqrt{17}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{90\sqrt{17}-225}{68-10\sqrt{17}+10\sqrt{17}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{90\sqrt{17}-225}{43}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{17}-5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 45 } \cdot \left( 2 \sqrt{17}-5\right) = \color{blue}{45} \cdot 2 \sqrt{17}+\color{blue}{45} \cdot-5 = \\ = 90 \sqrt{17}-225 $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{17} + 5\right) } \cdot \left( 2 \sqrt{17}-5\right) = \color{blue}{ 2 \sqrt{17}} \cdot 2 \sqrt{17}+\color{blue}{ 2 \sqrt{17}} \cdot-5+\color{blue}{5} \cdot 2 \sqrt{17}+\color{blue}{5} \cdot-5 = \\ = 68- 10 \sqrt{17} + 10 \sqrt{17}-25 $$ |
| ③ | Simplify numerator and denominator |
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