Question

solve 6/x -4 = 4/x for x and determine if the solution is extraneous or not. x = −8, extraneous x = −8, non-extraneous x = 8, extraneous x = 8, non-extraneous

Answer 1

$\frac{6}{x-4} = \frac{4}{x} \\ 6x=4(x-4)=4x-16 \\ 2x=-16 \\ x=-8$
To check: 6/(-8-4) = 4/-8
6/-12 = 4/-8
1/-2 = 1/-2
Therefore, x = −8, non-extraneous