Solve 6 over x minus 6 equals the quantity of x over x minus 6, minus six halves. for x, and determine if the solution is extraneous or not.

6/(x - 6) = x/(x - 6) - 6/2
6/(x - 6) = x/(x - 6) - 3
6 = x - 3(x - 6)
6 = x - 3x + 18
-12 = -2x
x = 6
However, substituting x = 6 makes the denominator equal to zero, the this is an extraneous solution.