ax+(a-1)=(a+1)x

Solution for ax+(a-1)=(a+1)x equation:

Simplifying
ax + (a + -1) = (a + 1) * x

Reorder the terms:
ax + (-1 + a) = (a + 1) * x

Remove parenthesis around (-1 + a)
ax + -1 + a = (a + 1) * x

Reorder the terms:
-1 + a + ax = (a + 1) * x

Reorder the terms:
-1 + a + ax = (1 + a) * x

Reorder the terms for easier multiplication:
-1 + a + ax = x(1 + a)
-1 + a + ax = (1 * x + a * x)

Reorder the terms:
-1 + a + ax = (ax + 1x)
-1 + a + ax = (ax + 1x)

Add '-1ax' to each side of the equation.
-1 + a + ax + -1ax = ax + -1ax + 1x

Combine like terms: ax + -1ax = 0
-1 + a + 0 = ax + -1ax + 1x
-1 + a = ax + -1ax + 1x

Combine like terms: ax + -1ax = 0
-1 + a = 0 + 1x
-1 + a = 1x

Solving
-1 + a = 1x

Solving for variable 'a'.

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

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

Combine like terms: -1 + 1 = 0
0 + a = 1 + 1x
a = 1 + 1x

Simplifying
a = 1 + 1x