Rút gọn: 1/5x - 10 - 2x/x^2 - 4

To simplify the expressions:

1) 1/5x - 10 - 2x/(x^2 - 4)

First, factor the denominator x^2 - 4 to (x + 2)(x - 2):

1/5x - 10 - 2x/((x + 2)(x - 2))

Now, find a common denominator for the fractions:

1/5x - 10(x + 2)(x - 2)/(5x(x + 2)(x - 2)) - 2x(5x)/(5x(x + 2)(x - 2))

Combine the fractions:

(1 - 10(x + 2)(x - 2) - 10x^2)/(5x(x + 2)(x - 2))

Expand and simplify:

(1 - 10(x^2 - 4) - 10x^2)/(5x(x + 2)(x - 2))
(1 - 10x^2 + 40 - 10x^2)/(5x(x + 2)(x - 2))
(41 - 20x^2)/(5x(x + 2)(x - 2))

Therefore, the simplified expression is (41 - 20x^2)/(5x(x + 2)(x - 2)).

2) (3x + 1)/(xy) + (2x + 1)/(xy)

Combine the fractions:

(3x + 1 + 2x + 1)/(xy)
(5x + 2)/(xy)

Therefore, the simplified expression is (5x + 2)/(xy).