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).