Question

Solve 6 over x minus 4 equals 4 over x for x and determine if the solution is extraneous or not.

Answer 1

x=-8 is not extraneous.

Explanation:

The given equation is :

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

On cross multiplying the terms, we get

`6x=4(x-4)`

⇒
`6x=4x-16`

⇒
`6x-4x=-16`

⇒
`2x=-16`

⇒
`x=(-16)/(2)`

⇒
`x=-8`

Now, Extraneous is the point which is not included in the domain of the function but x=-8 is included in the domain of the given function.

Thus, x=-8 is not extraneous.

Answer 2

x= -8 not extraneous.

Explanation:

We have been given the expression:

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

We will cross multiply the terms we get:

`6x=4(x-4)`

Now, we will simplify we get:

`6x=4x-16`

`6x-4x=-16`

`2x=-16`

`x=-(16)/(2)`

`x=-8`

Extraneous is the point which is not included in the domain of the function.

-8 is not extraneous.