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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

Respuesta :

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

Answer:

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

Step-by-step explanation:

We have been given a function:

[tex]\frac{6}{x-4}=\frac{4}{x}[/tex]

We need to solve the expression for x

Firstly, we will cross multiply we get:

[tex]6x=4(x-4)[/tex]

[tex]\Rightarrow6x=4x-16[/tex]

[tex]\Rightarrow 2x=-16[/tex]

[tex]\Rightarrow x=-8[/tex]

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.


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