Rút gọn biểu thức: A = (1/2√x+2 + 1/√x+2) ÷ 1/(√x-2)²

To simplify the expression, we can start by simplifying the numerator and denominator separately.

Numerator:
A = ((1/2√x + 2) + (1/√x + 2))

To combine the fractions, we need a common denominator. The common denominator here is (√x + 2)(2√x + 2).

So, the numerator becomes:
A = ((1(2√x + 2) + 1(√x + 2))/(√x + 2)(2√x + 2))

Simplifying the numerator further:
A = (2√x + 2 + √x + 2)/(√x + 2)(2√x + 2)
A = (3√x + 4)/(√x + 2)(2√x + 2)

Denominator:
A = 1/(√x - 2)²

Now, we can rewrite the expression as:
A = (3√x + 4)/(√x + 2)(2√x + 2) * 1/(√x - 2)²

To simplify further, we can multiply the numerator and denominator together:
A = (3√x + 4)/(√x + 2)(2√x + 2) * 1/(√x - 2)(√x - 2)

Now, we can cancel out common factors:
A = (3√x + 4)/(√x + 2)(2√x + 2) * 1/(√x - 2)(√x - 2)
A = (3√x + 4)/(√x + 2)(√x - 2)(2√x + 2)

Therefore, the simplified expression is (3√x + 4)/(√x + 2)(√x - 2)(2√x + 2).