Answer
$$\frac{7}{5-\sqrt{7}}=\frac{35+7\sqrt{7}}{18}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7}{5-\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7}{5-\sqrt{7}}\frac{5+\sqrt{7}}{5+\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{35+7\sqrt{7}}{25+5\sqrt{7}-5\sqrt{7}-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{35+7\sqrt{7}}{18}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 + \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 } \cdot \left( 5 + \sqrt{7}\right) = \color{blue}{7} \cdot5+\color{blue}{7} \cdot \sqrt{7} = \\ = 35 + 7 \sqrt{7} $$ Simplify denominator. $$ \color{blue}{ \left( 5- \sqrt{7}\right) } \cdot \left( 5 + \sqrt{7}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot \sqrt{7}\color{blue}{- \sqrt{7}} \cdot5\color{blue}{- \sqrt{7}} \cdot \sqrt{7} = \\ = 25 + 5 \sqrt{7}- 5 \sqrt{7}-7 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator