(x-y+1)-(x+y-1)=0

Solution for (x-y+1)-(x+y-1)=0 equation:

Simplifying
(x + -1y + 1) + -1(x + y + -1) = 0

Reorder the terms:
(1 + x + -1y) + -1(x + y + -1) = 0

Remove parenthesis around (1 + x + -1y)
1 + x + -1y + -1(x + y + -1) = 0

Reorder the terms:
1 + x + -1y + -1(-1 + x + y) = 0
1 + x + -1y + (-1 * -1 + x * -1 + y * -1) = 0
1 + x + -1y + (1 + -1x + -1y) = 0

Reorder the terms:
1 + 1 + x + -1x + -1y + -1y = 0

Combine like terms: 1 + 1 = 2
2 + x + -1x + -1y + -1y = 0

Combine like terms: x + -1x = 0
2 + 0 + -1y + -1y = 0
2 + -1y + -1y = 0

Combine like terms: -1y + -1y = -2y
2 + -2y = 0

Solving
2 + -2y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -2y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2y = 0 + -2
-2y = 0 + -2

Combine like terms: 0 + -2 = -2
-2y = -2

Divide each side by '-2'.
y = 1

Simplifying
y = 1