Question
Answer
$$\dfrac{16}{\sqrt{14}-5}=-\dfrac{16\sqrt{14}+80}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{16}{\sqrt{14}-5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{16}{\sqrt{14}-5}\frac{\sqrt{14}+5}{\sqrt{14}+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16\sqrt{14}+80}{14+5\sqrt{14}-5\sqrt{14}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{16\sqrt{14}+80}{-11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{16\sqrt{14}+80}{11}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{14} + 5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 16 } \cdot \left( \sqrt{14} + 5\right) = \color{blue}{16} \cdot \sqrt{14}+\color{blue}{16} \cdot5 = \\ = 16 \sqrt{14} + 80 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{14}-5\right) } \cdot \left( \sqrt{14} + 5\right) = \color{blue}{ \sqrt{14}} \cdot \sqrt{14}+\color{blue}{ \sqrt{14}} \cdot5\color{blue}{-5} \cdot \sqrt{14}\color{blue}{-5} \cdot5 = \\ = 14 + 5 \sqrt{14}- 5 \sqrt{14}-25 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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