Answer
$$\frac{12\sqrt{3}+12\sqrt{7}+6\sqrt{21}+12\sqrt{3}-4\sqrt{63}-4\sqrt{147}-14\sqrt{21}-4\sqrt{63}}{1}=-4\sqrt{3}-12\sqrt{7}-8\sqrt{21}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12\sqrt{3}+12\sqrt{7}+6\sqrt{21}+12\sqrt{3}-4\sqrt{63}-4\sqrt{147}-14\sqrt{21}-4\sqrt{63}}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}24\sqrt{3}+12\sqrt{7}-8\sqrt{21}-8\sqrt{63}-4\sqrt{147} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24\sqrt{3}+12\sqrt{7}-8\sqrt{21}-24\sqrt{7}-28\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-4\sqrt{3}-12\sqrt{7}-8\sqrt{21}\end{aligned} $$ | |
| ① | Remove 1 from denominator. |
| ② | $$ - 8 \sqrt{63} =
-8 \sqrt{ 3 ^2 \cdot 7 } =
-8 \sqrt{ 3 ^2 } \, \sqrt{ 7 } =
-8 \cdot 3 \sqrt{ 7 } =
-24 \sqrt{ 7 } $$ |
| ③ | $$ - 4 \sqrt{147} =
-4 \sqrt{ 7 ^2 \cdot 3 } =
-4 \sqrt{ 7 ^2 } \, \sqrt{ 3 } =
-4 \cdot 7 \sqrt{ 3 } =
-28 \sqrt{ 3 } $$ |
| ④ | Combine like terms |
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