Rút gọn: 1/(3 - 2√2) + 1/(2 + √5), 1/(√3 + √7) + 2/(1 - √7), (a - 2√a)/(2 - √a), (x√y + y√x)/(√x + √y)

Sure, I can help you with these expressions. Let's simplify each one step by step:

1. (1/3 - 2√2) + (1/2 + √5)
To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6. So, we can rewrite the expression as:
(2/6 - 12√2/6) + (3/6 + 6√5/6)
Simplifying the fractions:
(-10√2/6) + (9/6 + 6√5/6)
Combining like terms:
(-10√2 + 9 + 6√5)/6

2. (1/√3 + √7) + (2/1 - √7)
To add these fractions, we need a common denominator. The least common multiple of 1 and √3 is √3. So, we can rewrite the expression as:
(√3/3 + √21/√3) + (2√3/√3 - √7)
Simplifying the fractions:
(2√3 + √21)/√3 + (2√3 - √7)
Combining like terms:
(4√3 + √21 - √7)/√3

3. (a - 2√a)/(2 - √a)
To simplify this expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (2 + √a):
[(a - 2√a)(2 + √a)] / [(2 - √a)(2 + √a)]
Simplifying the numerator:
(2a + a√a - 4√a - 2a) / (4 - a)
Combining like terms:
(a√a - 4√a) / (4 - a)

4. (x√y + y√x) / (√x + √y)
To simplify this expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (√x - √y):
[(x√y + y√x)(√x - √y)] / [(√x + √y)(√x - √y)]
Simplifying the numerator:
(x√xy - xy - y√xy + yx) / (x - y)
Combining like terms:
(x√xy - y√xy + xy) / (x - y)

I hope this helps! Let me know if you have any further questions.