Answer
$$\frac{10}{-7+\sqrt{11}}=\frac{-70-10\sqrt{11}}{38}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10}{-7+\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10}{-7+\sqrt{11}}\frac{-7-\sqrt{11}}{-7-\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-70-10\sqrt{11}}{49+7\sqrt{11}-7\sqrt{11}-11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-70-10\sqrt{11}}{38}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ -7- \sqrt{11}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 } \cdot \left( -7- \sqrt{11}\right) = \color{blue}{10} \cdot-7+\color{blue}{10} \cdot- \sqrt{11} = \\ = -70- 10 \sqrt{11} $$ Simplify denominator. $$ \color{blue}{ \left( -7 + \sqrt{11}\right) } \cdot \left( -7- \sqrt{11}\right) = \color{blue}{-7} \cdot-7\color{blue}{-7} \cdot- \sqrt{11}+\color{blue}{ \sqrt{11}} \cdot-7+\color{blue}{ \sqrt{11}} \cdot- \sqrt{11} = \\ = 49 + 7 \sqrt{11}- 7 \sqrt{11}-11 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator