Câu a:
A = (√y / (x + √xy)) + (√y / (x - √xy)) - (2√y) / (x - y)
= (√y * (x - √xy) + √y * (x + √xy)) / ((x + √xy)(x - √xy)) - (2√y) / (x - y)
= (2x√y) / (x^2 - xy) - (2√y) / (x - y)
= (2√y) / (x(x - y)) - (2√y) / (x - y)
= (2√y - 2x√y) / (x(x - y))
= (-2√y(x - 1)) / (x(x - y))
Câu b:
√(x - 1)^2 + √(x - 3)^2 = |x - 1| + |x - 3|
Vì 1 < x < 3 nên x - 1 > 0 và x - 3 < 0. Do đó:
= (x - 1) + (3 - x)
= 2
Câu c:
B = (√x / (√x - 3)) + (√x / (√x + 3)) * ((x - 9) / (3√x))
= (√x * (√x + 3) + √x * (√x - 3)) / ((√x - 3)(√x + 3)) * ((x - 9) / (3√x))
= (2x) / (x - 9) * ((x - 9) / (3√x))
= (2√x) / 3
Câu d:
C = (1 + (a + √a) / √a) * (1 / a) * (1 - (a - √a) / (√a - 1))
= ((√a + a + √a) / √a) * (1 / a) * ((√a - 1 - a + √a) / (√a - 1))
= ((2√a + a) / √a) * (1 / a) * ((2√a - a - 1) / (√a - 1))
= ((√a + 1)^2 / √a) * (1 / a) * ((√a - 1)^2 / (√a - 1))
= (√a + 1) / a