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

Option 2nd is correct that is x= -8 and non-extraneous.

Explanation:

We have been given a function:

`(6)/(x-4)=(4)/(x)`

We need to solve the expression for x

Firstly, we will cross multiply we get:

`6x=4(x-4)`

`\Rightarrow6x=4x-16`

`\Rightarrow 2x=-16`

`\Rightarrow x=-8`

Extraneous is the point where the function becomes not defined.

Hence, when we substitute x=-8 in the given function

Function remains defined hence, x=-8 is non-extraneous

Therefore, Option 2nd is correct that is x= -8 and non-extraneous.

Answer 2

`(6)/(x-4) = (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