Carcass wrote:
\(\frac{4(\sqrt{6} + \sqrt{2})}{\sqrt{6}-\sqrt{2}} - \frac{2+\sqrt{3}}{2-\sqrt{3}} =\)
A. \(1\)
B. \(\sqrt{6} - \sqrt{2}\)
C. \(\sqrt{6} + \sqrt{2}\)
D. \(8\)
E. \(12\)
We can rationalize each term as follows:
4(√6 + √2)/(√6 - √2) = 4(√6 + √2)(√6 + √2)/(√6 - √2)(√6 + √2)
= 4[6 + 2 + 2√6√2]/[6 - 2]
= 8 + 4√3
(2 + √3)/(2 - √3) = (2 + √3)(2 + √3)/(2 - √3)(2 + √3)
= [4 + 3 + 2(2)(√3)]/[4 - 3]
= 7 + 4√3
Thus, subtracting, we have: 1
Answer A
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