Let two non-zero variables, (a) and (b), be equal to each other:
(a = b)
· Multiply both sides by (a):
(a^2 = ab)
· Subtract b^2 from both sides:
a^2 - b^2=ab - b^2
· Factor both sides:
(a - b)(a + b) = b(a - b)
· Divide both sides by ((a - b)):
(a + b = b)
· Substitute (a) with (b) (since (a = b)):
(b + b = b)
(2b = b)
· Divide both sides by (b):
(2 = 1)
· Add 1 to both sides:
(3 = 2)
· Substitute ((1 + 1)) back in for 2:
(3 = 1 + 1)