Question

How do you solve `3/(x-3) + 4/x +1/3 = x/(x-3)` and find any extraneous solutions?

Answer 1

`x=6`

Explanation:

`3/(x-3)+4/x+1/3=x/(x-3)`

`4/x+1/3=(x-3)/(x-3)`

I assumed `x!=3`, because `x=3` is extraneous solution. Hence,

`4/x+1/3=1`

`4/x=2/3`

`x=3*4/2=6`