1) To simplify the expression (2x+1-1/1-2x):(2x-4x^2/2x+1), we can start by simplifying each fraction separately.

The first fraction (2x+1-1/1-2x) can be simplified as follows:
(2x+1-1)/(1-2x)
(2x)/(1-2x)
Now, let's simplify the second fraction (2x-4x^2/2x+1):
(2x-4x^2)/(2x+1)

Now, we can rewrite the original expression as:
(2x)/(1-2x) : (2x-4x^2)/(2x+1)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
(2x)/(1-2x) * (2x+1)/(2x-4x^2)

Next, we can simplify the expression by canceling out common factors:
(2x)/(1-2x) * (2x+1)/(2x(1-2x))
(2x+1)/(2x)

Therefore, the simplified expression is (2x+1)/(2x).

2) To simplify the expression 4xy/y^2-x^2:(1/y^2-x^2+1/x^2+2xy+y^2), we can start by simplifying each fraction separately.

The first fraction 4xy/y^2-x^2 can be simplified as follows:
4xy/(y^2-x^2)

Now, let's simplify the second fraction 1/y^2-x^2+1/x^2+2xy+y^2:
1/(y^2-x^2) + 1/(x^2+2xy+y^2)

To add fractions, we need a common denominator. The common denominator for the two fractions is (y^2-x^2)(x^2+2xy+y^2).

Now, let's rewrite the expression with the common denominator:
(1(x^2+2xy+y^2))/(y^2-x^2)(x^2+2xy+y^2) + (1(y^2-x^2))/(y^2-x^2)(x^2+2xy+y^2)

Simplifying further, we get:
(x^2+2xy+y^2 + y^2-x^2)/(y^2-x^2)(x^2+2xy+y^2)
(2y^2 + 2xy)/(y^2-x^2)(x^2+2xy+y^2)

Now, let's rewrite the original expression as:
4xy/(y^2-x^2) : (2y^2 + 2xy)/(y^2-x^2)(x^2+2xy+y^2)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
4xy/(y^2-x^2) * (y^2-x^2)(x^2+2xy+y^2)/(2y^2 + 2xy)

Next, we can simplify the expression by canceling out common factors:
4xy(x^2+2xy+y^2)/(2y^2 + 2xy)
2xy(x^2+2xy+y^2)/(y^2 + xy)

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