Question

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Answer 1

$8- \sqrt{12}+ \frac{2 \sqrt{12}\cdot \sqrt{5} }{12 \sqrt{5}-5 \sqrt{12} }- \sqrt{5}= \\ \\ = \frac{(8- \sqrt{12})\cdot (12 \sqrt{5}-5 \sqrt{12})+ 2 \sqrt{12}\cdot \sqrt{5}- \sqrt{5}\cdot (12 \sqrt{5}-5 \sqrt{12}) }{12 \sqrt{5}-5 \sqrt{12} } = \\ \\ = \frac{96 \sqrt{5}-12 \sqrt{12}\cdot \sqrt{5}-40 \sqrt{12}+5 \sqrt{12}\cdot \sqrt{12}+2 \sqrt{12}\cdot \sqrt{5}-12 \sqrt{5}\cdot \sqrt{5}-5 \sqrt{5}\cdot \sqrt{12}}{12 \sqrt{5}-5 \sqrt{12} }=$

$=\frac{96 \sqrt{5}-12 \sqrt{60}-40 \sqrt{12}+5 \cdot12+2 \sqrt{60}-12 \cdot 5-5 \sqrt{60}}{12 \sqrt{5}-5 \sqrt{12} }= \frac{96 \sqrt{5}-15 \sqrt{60}-40 \sqrt{12}}{12 \sqrt{5}-5 \sqrt{12} }$