(a-b)x+(a+b)x=2

Solution for (a-b)x+(a+b)x=2 equation:

Simplifying
(a + -1b) * x + (a + b) * x = 2

Reorder the terms for easier multiplication:
x(a + -1b) + (a + b) * x = 2
(a * x + -1b * x) + (a + b) * x = 2
(ax + -1bx) + (a + b) * x = 2

Reorder the terms for easier multiplication:
ax + -1bx + x(a + b) = 2
ax + -1bx + (a * x + b * x) = 2
ax + -1bx + (ax + bx) = 2

Reorder the terms:
ax + ax + -1bx + bx = 2

Combine like terms: ax + ax = 2ax
2ax + -1bx + bx = 2

Combine like terms: -1bx + bx = 0
2ax + 0 = 2
2ax = 2

Solving
2ax = 2

Solving for variable 'a'.

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

Divide each side by '2x'.
a = x-1

Simplifying
a = x-1