Rút gọn

A = √a/√a+√b + a/b-a) / (√a/√a+√b + a/a+b+2√ab) - a+b+2√ab/b-a

To simplify this expression, let's start by finding a common denominator for the fractions in the numerator and denominator.

The common denominator for the fractions in the numerator is (b - a)(√a + √b), and for the fractions in the denominator is (b - a)(a + b + 2√ab).

Now, let's simplify the expression using the common denominator:

A = (√a(b - a) + a(√a + √b)) / (√a(b - a) + a(a + b + 2√ab)) - (a + b + 2√ab)(b - a) / (b - a)(a + b + 2√ab)

Simplifying further:

A = (√ab - a√a + a√a + a√b) / (√ab - a√a + a√a + a√b + a^2 + ab + 2a√ab - ab + a^2 - 2a√ab)

The terms with √a cancel out:

A = (√ab + a√b) / (√ab + a√b + a^2 + ab + a^2 - ab)

Simplifying again:

A = (√ab + a√b) / (2a^2 + 2√ab)

Finally, we can factor out a common term from the numerator:

A = (√ab(1 + a)) / (2a^2 + 2√ab)

Therefore, the simplified expression is A = (√ab(1 + a)) / (2a^2 + 2√ab).