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

Answer:

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

Step-by-step explanation:

We have been given a function:

$\frac{6}{x-4}=\frac{4}{x}$

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

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