Rút gọn A

To simplify the expression A = 2/x + y√3(x+y)^2/4, we can start by simplifying the second term.

Let's simplify y√3(x+y)^2/4:

First, we can simplify (x+y)^2 by expanding it:
(x+y)^2 = (x+y)(x+y) = x(x+y) + y(x+y) = x^2 + xy + xy + y^2 = x^2 + 2xy + y^2

Now, let's substitute this back into the expression:
y√3(x+y)^2/4 = y√3(x^2 + 2xy + y^2)/4

Next, let's simplify the entire expression A = 2/x + y√3(x+y)^2/4:

A = 2/x + y√3(x^2 + 2xy + y^2)/4

To simplify the first term, we can multiply it by x/x to get a common denominator:
2/x = (2/x)(x/x) = 2x/x^2 = 2x^2/x^2

Now, let's substitute this back into the expression:
A = 2x^2/x^2 + y√3(x^2 + 2xy + y^2)/4

Now, let's simplify the expression further:
A = 2x^2/x^2 + y√3(x^2 + 2xy + y^2)/4
= 2 + y√3(x^2 + 2xy + y^2)/4

Therefore, the simplified expression is A = 2 + y√3(x^2 + 2xy + y^2)/4.