Question
Answer
$$\dfrac{\sqrt{7}}{3\sqrt{2}-4\sqrt{3}}=-\dfrac{3\sqrt{14}+4\sqrt{21}}{30}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{7}}{3\sqrt{2}-4\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{7}}{3\sqrt{2}-4\sqrt{3}}\frac{3\sqrt{2}+4\sqrt{3}}{3\sqrt{2}+4\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{14}+4\sqrt{21}}{18+12\sqrt{6}-12\sqrt{6}-48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{14}+4\sqrt{21}}{-30} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{3\sqrt{14}+4\sqrt{21}}{30}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{2} + 4 \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{7} } \cdot \left( 3 \sqrt{2} + 4 \sqrt{3}\right) = \color{blue}{ \sqrt{7}} \cdot 3 \sqrt{2}+\color{blue}{ \sqrt{7}} \cdot 4 \sqrt{3} = \\ = 3 \sqrt{14} + 4 \sqrt{21} $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{2}- 4 \sqrt{3}\right) } \cdot \left( 3 \sqrt{2} + 4 \sqrt{3}\right) = \color{blue}{ 3 \sqrt{2}} \cdot 3 \sqrt{2}+\color{blue}{ 3 \sqrt{2}} \cdot 4 \sqrt{3}\color{blue}{- 4 \sqrt{3}} \cdot 3 \sqrt{2}\color{blue}{- 4 \sqrt{3}} \cdot 4 \sqrt{3} = \\ = 18 + 12 \sqrt{6}- 12 \sqrt{6}-48 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
This page was created using
Rationalize Denominator Calculator