Question

How do you solve `x/(x+4)=2/x` and check for extraneous solutions?

Answer 1

`x in {4, -2}`

Explanation:

Multiply both sides.

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

`x^2 = 2x + 8`

`x^2 - 2x - 8 = 0`

Sum `= 2`, Product = `-8`, therefore `x = 4 or x = -2`

The extraneous ones would be `x = 0 or x = -4`, because there would be zero denominator.