Question

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.

Answer 1

Let's write that out symbolically:

   6             x       6
------  = --------- - ---
 x -6          x-6      2

The LCD is 2(x-6).  Modifying this equation appropriately, 

  2(6)         2(x)       2(x-6)
--------- = --------- - -----------
2(x-6)      2(x-6)       2(x-6)

Then 12 = 2x - 2x + 12    This is true for all x, so there are an infinite number of solutions, EXCEPT that x = 6 is not a solution (causes div. by zero).