Question

Rationalise (√7-1/√7+1)-(√7+1/√7-1)=a+b√7

Answer 1

your answer is in the attachment..

Answer 2

$(\frac{ \sqrt{7} - 1 }{ \sqrt{7} + 1 } \times \frac{ \sqrt{7} - 1}{ \sqrt{7} - 1 }) - ( \frac{ \sqrt{7} + 1}{ \sqrt{7} - 1 } \times \frac{ \sqrt{7} + 1}{ \sqrt{7} + 1 }) = a + b \sqrt{7} \\ \frac{ { (\sqrt{7} - 1 })^{2} }{( { \sqrt{7} })^{2} - ({1})^{2} } - \frac{ { (\sqrt{7} + 1 })^{2} }{( { \sqrt{7} })^{2} - {(1)}^{2} } = a + b \sqrt{7} \\ \frac{( { \sqrt{7} })^{2} + 2 \sqrt{7} - 1 }{6} - \frac{( { \sqrt{7} })^{2} +2 \sqrt{7} + ( {1})^{2}}{6} = a + b \sqrt{7} \\ \frac{7 + 2 \sqrt{7} - 1 - 7 + 2 \sqrt{7} + 1}{6} = a + b \sqrt{7} \\ \frac{0 + 4 \sqrt{7} }{6} = a + b \sqrt{7} \\ a = \frac{0}{6} = 0 \\ b = \frac{4}{6} \sqrt{7} = \frac{2}{3}$