1)
1/ 6√7 = √7/(6*7) = √7/42
6 / (√5-1) = (5 -1) / (√5-1) = ((√5)² - 1² ) /(√5-1) =
= [ (√5-1)(√5+1) ] / (√5 -1) =
= ( √5 +1 )/1= √5 +1
2)
(3+√3)/(√6+√2) = [√3(√3+1) ] / [ √2 (√3 +1) ] =
= √3/√2 = (√3 *√2 ) / (√2*√2) = √6/2
(4-b) / (2-√b) = (2² - (√b)² ) / (2-√b) =
=(2-√b)(2+√b) / (2-√b) = (2+√b)/1 = 2+√b
3) 3/(5√2 +1) - 3/(5√2 -1) =
= [3(5√2 -1) - 3(5√2+1) ] / [(5√2+1)(5√2-1)]=
= [ 15√2 - 3 -15√2 -3 ] / [ (5√2)² - 1² ] =
= -6 / (50-1) = -6/49