Question

Solve 4 over x plus 2 equals 2 over x for x and determine if the solution is extraneous or not.

x = -2, extraneous

x = -2, non-extraneous

x = 2, extraneous

x = 2, non-extraneous

Answer 1

The solution is x=2 , non-extraneous

Explanation:

Answer 2

The solution is x=2 and non-extraneous.

D is correct.

Explanation:

Given:
`(4)/(x+2)=(2)/(x)`

We need to solve for x.

Here we have rational expression both sides and to solve for x.

`(4)/(x+2)=(2)/(x)`

Cross multiply both sides

`4x=2(x+2)`

`4x=2x+4`

`4x-2x=4`

`2x=4`

`x=2`

Now, we will check the extraneous solution. Put x=2 into original equation.

`(4)/(2+2)=(2)/(2)`

`(4)/(4)=(2)/(2)`

`1=1`

Correct solution.

Hence, The solution is x=2 and non-extraneous.