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- Feb 14, 2012

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- Feb 14, 2012

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\(\displaystyle \frac{(x-1)(x-3)+(x+1)\sqrt{(x+3)(x-3)}}{(x+1)(x+3)+(x-1)\sqrt{(x+3)(x-3)}}\)

Factoring further, we obtain:

\(\displaystyle \frac{\sqrt{x-3}((x-1)\sqrt{x-3}+(x+1)\sqrt{x+3})}{\sqrt{x+3}((x+1)\sqrt{x+3}+(x-1)\sqrt{x-3})}\)

Dividing out the common factors, we are left with:

\(\displaystyle \sqrt{\frac{x-3}{x+3}}\)

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Bravo, Mark!