n-(n-1)=1-(1-n)

Solution for n-(n-1)=1-(1-n) equation:

Simplifying
n + -1(n + -1) = 1 + -1(1 + -1n)

Reorder the terms:
n + -1(-1 + n) = 1 + -1(1 + -1n)
n + (-1 * -1 + n * -1) = 1 + -1(1 + -1n)
n + (1 + -1n) = 1 + -1(1 + -1n)

Reorder the terms:
1 + n + -1n = 1 + -1(1 + -1n)

Combine like terms: n + -1n = 0
1 + 0 = 1 + -1(1 + -1n)
1 = 1 + -1(1 + -1n)
1 = 1 + (1 * -1 + -1n * -1)
1 = 1 + (-1 + 1n)

Combine like terms: 1 + -1 = 0
1 = 0 + 1n
1 = 1n

Solving
1 = 1n

Solving for variable 'n'.

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

Add '-1n' to each side of the equation.
1 + -1n = 1n + -1n

Combine like terms: 1n + -1n = 0
1 + -1n = 0

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1