Question

(8.02 LC)

Solve 6/x-6 = x/x-6 - 6/2 for x and determine if the solution is extraneous or not.


A. x = −6, extraneous

B. x = −6, non-extraneous

C . x = 6, non-extraneous

D. x = 6, extraneous

Answer 1

I just took the test

Explanation:

x= 6; extraneous

Answer 2

First multiply by the LCM for the denominators (in this case 2*(x-6))
Solve for x:
12=2x-6(x-6)
12=2x-6x+36
12=-4x+36
4x=24
x=6
And plug x back in to the original equation:
6/(6-6)=6/(6-6)-6/2
6/0=6/0-6/2
As you can see, it is extraneous, since it is impossible to divide by zero