Find the values of `a` and `b:(7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5))=a+sqrt(5)b`

Explanation

We have
`(7+ 3sqrt(5))/(3+ sqrt(5)) = (7- 3sqrt(5))/(3- sqrt(5))= (( 7 + 3 sqrt(5)))/((3+sqrt(5))) - ((7 - 3sqrt(5)))/((3-sqrt(5))) xx ((3+ sqrt(5)))/((3+sqrt(5)))`
` = ((21 - 7 sqrt(5) + 9 sqrt(5) - 15))/((3 + sqrt(5))(3-sqrt(5))) - ((21 + 7 sqrt(5) - 9sqrt(5) - 15))/((3-sqrt(5))(3+sqrt(5)))`
`= ((6 + 2sqrt(5)))/((3)^(2) -(sqrt(5))^(2)) - ((6 - 2sqrt(5)))/((3)^(2) - (sqrt(5))^(2))`
`(( 6 + 2 sqrt(5)))/((9-5)) - (( 6 - 2sqrt(5)))/((9-5)) = ( 6 + 2 sqrt(5))/(4) - (6-2sqrt(5))/(4)`
` = (5+ 2sqrt(5) - 6 + 2sqrt(5))/(4) = (4sqrt(5))/(4) = sqrt(5)`
`therefore (7+ 3sqrt(5))/(3+ sqrt(5)) - (7-3sqrt(5))/(3- sqrt(5)) = a + sqrt(5b) rArr sqrt(5) = a + sqrt(5b)`
`rArr a = 0 and b = 1`.