Bentuk sederhana dari (akar 3 + akar 7)(akar 3 - akar 7) per 2 akar 5 - 4 akar 2

[tex] \frac{( \sqrt{3} + \sqrt{7} )( \sqrt{3} - \sqrt{7} )}{2 \sqrt{5} - 4 \sqrt{2} } \\ = \frac{3 + \sqrt{21} - \sqrt{21} - 7 }{2 \sqrt{5} - 4 \sqrt{2} } \times \frac{2 \sqrt{5} + 4 \sqrt{2} }{2 \sqrt{5} + 4 \sqrt{2} } \\ = \frac{3 - 0 - 7}{2 \sqrt{5} - 4 \sqrt{2} } \times \frac{2 \sqrt{5} + 4 \sqrt{2} }{2 \sqrt{5} + 4 \sqrt{2} } \\ = \frac{ - 4}{2 \sqrt{5} - 4 \sqrt{2} } \times \frac{2 \sqrt{5} + 4 \sqrt{2} }{2 \sqrt{5} + 4 \sqrt{2} } \\ = \frac{ - 8 \sqrt{5} - 16 \sqrt{2} }{4 \times 5 - 16 \times 4} \\ = \frac{ - 8 \sqrt{5} - 16 \sqrt{2} }{20 - 64} \\ = \frac{ - 8 \sqrt{5} - 16 \sqrt{2} }{ - 44} \\ = \frac{2 \sqrt{5} + 4 \sqrt{2} }{11} [/tex]