<s>[INST] How can one simplify the following expression? I have the expression:
$$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8}{3} \sqrt{b^{2}c^{2}A^{2} + a^{2}c^{2}B^{2} + a^{2}b^{2}C^{2} - abc^{2}AB - ab^{2}cAC - a^{2}bcBC}$$
and I would like to be able to simplify it, if it is at all possible.
Thank you.
 [/INST] $$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8}{3} \sqrt{{a^2b^2c^2}\left(\frac{A^2}{a^2} +\frac{B^2}{b^2}  + \frac{C^2}{c^2} - \frac{AB}{ab} - \frac{AC}{ac} - \frac{BC}{bc}\right)},$$
$$-\left(\frac{A}{3a} + \frac{B}{3b} + \frac{C}{3c}\right) \pm \frac{8|abc|}{3} \sqrt{\frac{A^2}{a^2} +\frac{B^2}{b^2}  + \frac{C^2}{c^2} - \frac{AB}{ab} - \frac{AC}{ac} - \frac{BC}{bc}},$$
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