x = y (1) Assume x is equal y
x*x = x*y (2) Multiply both sides by x
x*x - y*y = x*y - y*y (3) Subtract y*y from both sides
(x-y)*(x+y) = (x-y)*y (4) Factor (x-y) from both sides
(x+y) = y (5) Cancel (x-y) from both sides
(x+x) = x (6) Since x=y from eq. (1), replace y with x
2x = x (7) Simplify
2 = 1 (8) Cancel x from both sides
AnswerFrom the fact that we cannot divide any number by zero, we can conclude the following:
Since x is equal to y (from Eq. 1), canceling out x-y (which is equal to zero) to get to Equation 5 is not allowed. Remember, canceling out x-y is the same as dividing both sides of the equation by x-y, thereby performing a division by zero operation. Since an invalid operation is performed to get to Equation 5, all equations, including 2 = 1 (as we know), that are derived from Equation 5 are invalid.
I’m lost, whats an x? 🙂