a/ Rút gọn biểu thức A:

Ta có A = ((2+√a)²(√a +1)²) / (2√a+3) + (a+√a) / (√a+1)

= ((4 + 4√a + a)(a + 2√a + 1)) / (2√a + 3) + (a + √a) / (√a + 1)

= (4a + 8√a + 4 + 4a + 4√a + a) / (2√a + 3) + (a + √a) / (√a + 1)

= (8a + 12√a + 4) / (2√a + 3) + (a + √a) / (√a + 1)

= 4(2a + 3√a + 1) / (2√a + 3) + (a + √a) / (√a + 1)

= 4(2a + 3√a + 1) / (2√a + 3) + (√a(√a + 1)) / (√a + 1)

= 4(2a + 3√a + 1) / (2√a + 3) + √a

= 4(2a + 3√a + 1) / (2√a + 3) + √a(2√a + 2) / (2√a + 3)

= (4(2a + 3√a + 1) + 2√a(2√a + 2)) / (2√a + 3)

= (8a + 12√a + 4 + 4√a + 4) / (2√a + 3)

= (8a + 16√a + 8) / (2√a + 3)

= 8(a + 2√a + 1) / (2√a + 3)

= 8(√a + 1)² / (2√a + 3)

= 8(√a + 1)² / (2√a + 3)

Rút gọn biểu thức B:

Ta có B = ((√b + 1)² - 4√b) / (√b - 1)

= (b + 2√b + 1 - 4√b) / (√b - 1)

= (b - 2√b + 1) / (√b - 1)

= ((√b - 1)²) / (√b - 1)

= √b - 1

b/ Tính số trị của hiệu A - B khi a = 6 - 2√5, b = 6 + 2√5:

Đặt x = 6 - 2√5, y = 6 + 2√5

Thay x và y vào biểu thức A và B ta được:

A = 8(√(6 - 2√5) + 1)² / (2√(6 - 2√5) + 3)

B = √(6 + 2√5) - 1

Tính A - B:

A - B = 8(√(6 - 2√5) + 1)² / (2√(6 - 2√5) + 3) - √(6 + 2√5) + 1

= 8(√(6 - 2√5) + 1)² / (2√(6 - 2√5) + 3) - √(6 + 2√5) + 1 * (2√(6 + 2√5) - 1) / (2√(6 + 2√5) - 1)

= (8(√(6 - 2√5) + 1)² - (√(6 + 2√5) - 1)(2√(6 + 2√5) - 1)) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 2(6 + 2√5) - √5 - 1) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 12 - 4√5 - √5 - 1) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)² - 13 - 5√5) / (2√(6 - 2√5) + 3)

= (8(√(6 - 2√5) + 1)