3.
1) (a - 4)/(√a - 2) = ((√a - 2)(√a + 2))/(√a - 2) = √a + 2
2) (√23 - 23)/√23 = (√23 - (√23)²)/√23 = (√23(1 - √23))/√23 = 1 - √23
3) (a - 5)/(a + 2√(5a) + 5) = ((√a - √5)(√a + √5))/(√a + 5)² = √a - √5
4.
1) 8/(3√2) = (8√2)/(3·2) = (4√2)/3
2) 4/(√13 - 3) = (4(√13 + 3))/((√13 - 3)(√13 + 3)) = (4(√13 + 3))/(13 - 9) = (4(√13 + 3))/4 = √13 + 3
3) 3/(√14 + √5) = (3(√14 - √5))/((√14 + √5)(√14 - √5)) = (3(√14 - √5))/(14 - 5) = (3(√14 - √5))/9 = (√14 - √5)/3
