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.