Answer
$$\frac{-7}{-4+\sqrt{5}}=\frac{28+7\sqrt{5}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-7}{-4+\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-7}{-4+\sqrt{5}}\frac{-4-\sqrt{5}}{-4-\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{28+7\sqrt{5}}{16+4\sqrt{5}-4\sqrt{5}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28+7\sqrt{5}}{11}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -4- \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -7 } \cdot \left( -4- \sqrt{5}\right) = \color{blue}{-7} \cdot-4\color{blue}{-7} \cdot- \sqrt{5} = \\ = 28 + 7 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( -4 + \sqrt{5}\right) } \cdot \left( -4- \sqrt{5}\right) = \color{blue}{-4} \cdot-4\color{blue}{-4} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot-4+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5} = \\ = 16 + 4 \sqrt{5}- 4 \sqrt{5}-5 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator