Question
Answer
$$\dfrac{2}{3\sqrt{2}-5}=-\dfrac{6\sqrt{2}+10}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{3\sqrt{2}-5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{3\sqrt{2}-5}\frac{3\sqrt{2}+5}{3\sqrt{2}+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{2}+10}{18+15\sqrt{2}-15\sqrt{2}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{2}+10}{-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{6\sqrt{2}+10}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{2} + 5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( 3 \sqrt{2} + 5\right) = \color{blue}{2} \cdot 3 \sqrt{2}+\color{blue}{2} \cdot5 = \\ = 6 \sqrt{2} + 10 $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{2}-5\right) } \cdot \left( 3 \sqrt{2} + 5\right) = \color{blue}{ 3 \sqrt{2}} \cdot 3 \sqrt{2}+\color{blue}{ 3 \sqrt{2}} \cdot5\color{blue}{-5} \cdot 3 \sqrt{2}\color{blue}{-5} \cdot5 = \\ = 18 + 15 \sqrt{2}- 15 \sqrt{2}-25 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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