Answer
$$\frac{\sqrt{3}^2-\sqrt{3}-\sqrt{3}+1}{\sqrt{3}^2-\sqrt{3}+\sqrt{3}-1}=2-\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{3}^2-\sqrt{3}-\sqrt{3}+1}{\sqrt{3}^2-\sqrt{3}+\sqrt{3}-1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3-\sqrt{3}-\sqrt{3}+1}{3-\sqrt{3}+\sqrt{3}-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3-2\sqrt{3}+1}{3-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{3-2\sqrt{3}+1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{4-2\sqrt{3}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{2-\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}2-\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{3}^2 =
\sqrt{3} ^2 =
\lvert 3 \rvert =
3 $$ |
| ② | $$ \sqrt{3}^2 =
\sqrt{3} ^2 =
\lvert 3 \rvert =
3 $$ |
| ③ | Combine like terms |
| ④ | Combine like terms |
| ⑤ | Combine like terms |
| ⑥ | Simplify numerator and denominator |
| ⑦ | Divide both numerator and denominator by 2. |
| ⑧ | Remove 1 from denominator. |
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