Answer
$$\frac{6}{7\sqrt{5}-5}=\frac{42\sqrt{5}+30}{220}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{7\sqrt{5}-5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{7\sqrt{5}-5}\frac{7\sqrt{5}+5}{7\sqrt{5}+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{42\sqrt{5}+30}{245+35\sqrt{5}-35\sqrt{5}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{42\sqrt{5}+30}{220}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 7 \sqrt{5} + 5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( 7 \sqrt{5} + 5\right) = \color{blue}{6} \cdot 7 \sqrt{5}+\color{blue}{6} \cdot5 = \\ = 42 \sqrt{5} + 30 $$ Simplify denominator. $$ \color{blue}{ \left( 7 \sqrt{5}-5\right) } \cdot \left( 7 \sqrt{5} + 5\right) = \color{blue}{ 7 \sqrt{5}} \cdot 7 \sqrt{5}+\color{blue}{ 7 \sqrt{5}} \cdot5\color{blue}{-5} \cdot 7 \sqrt{5}\color{blue}{-5} \cdot5 = \\ = 245 + 35 \sqrt{5}- 35 \sqrt{5}-25 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator