Answer
$$\frac{14\sqrt{12}}{\sqrt{9}+4}=4\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{14\sqrt{12}}{\sqrt{9}+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{14\sqrt{12}}{\sqrt{9}+4}\frac{\sqrt{9}-4}{\sqrt{9}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{84\sqrt{3}-112\sqrt{3}}{9-12+12-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-28\sqrt{3}}{-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{28\sqrt{3}}{7} \xlongequal{ } \\[1 em] & \xlongequal{ }4\sqrt{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{9}-4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 14 \sqrt{12} } \cdot \left( \sqrt{9}-4\right) = \color{blue}{ 14 \sqrt{12}} \cdot \sqrt{9}+\color{blue}{ 14 \sqrt{12}} \cdot-4 = \\ = 84 \sqrt{3}- 112 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{9} + 4\right) } \cdot \left( \sqrt{9}-4\right) = \color{blue}{ \sqrt{9}} \cdot \sqrt{9}+\color{blue}{ \sqrt{9}} \cdot-4+\color{blue}{4} \cdot \sqrt{9}+\color{blue}{4} \cdot-4 = \\ = 9-12 + 12-16 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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