(x+1)+(x-1)=(x-1)*(x+1)

Solution for (x+1)+(x-1)=(x-1)*(x+1) equation:

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

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

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

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

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

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

Combine like terms: 1 + -1 = 0
0 + x + x = (x + -1)(x + 1)
x + x = (x + -1)(x + 1)

Combine like terms: x + x = 2x
2x = (x + -1)(x + 1)

Reorder the terms:
2x = (-1 + x)(x + 1)

Reorder the terms:
2x = (-1 + x)(1 + x)

Multiply (-1 + x) * (1 + x)
2x = (-1(1 + x) + x(1 + x))
2x = ((1 * -1 + x * -1) + x(1 + x))
2x = ((-1 + -1x) + x(1 + x))
2x = (-1 + -1x + (1 * x + x * x))
2x = (-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
2x = (-1 + 0 + x2)
2x = (-1 + x2)

Solving
2x = -1 + x2

Solving for variable 'x'.

Reorder the terms:
1 + 2x + -1x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
1 + 2x + -1x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
1 + 2x + -1x2 = 0 + x2 + -1x2
1 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x + x2 = 0 + 1
-2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2x + x2 = 1

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1 + 1

Reorder the terms:
1 + -2x + x2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2x + x2 = 2

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -1 = 1.414213562

Simplifying
x + -1 = 1.414213562

Reorder the terms:
-1 + x = 1.414213562

Solving
-1 + x = 1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.414213562 + 1
x = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
x = 2.414213562

Simplifying
x = 2.414213562

Subproblem 2
x + -1 = -1.414213562

Simplifying
x + -1 = -1.414213562

Reorder the terms:
-1 + x = -1.414213562

Solving
-1 + x = -1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.414213562 + 1
x = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
x = -0.414213562

Simplifying
x = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.414213562, -0.414213562}