Question

How do you solve `3/(x-3)-4=x/(x-3)` and check for extraneous solutions?

Answer 1

`x=3` is extraneous solution, so original equation has no solution.

Explanation:

`3/(x-3)-4=x/(x-3); x!=3` . Multiplying by `(x-3)` on both

sides we get, `3-4(x-3)=x or 3-4x+12=x` or

`5x =15 or x=3` Check : `3/(3-3)-4=x/(3-3)`

`f(x)` is undefined at `x=3` Therefore, it cannot be a root of the

original equation. `x=3` extraneous solution, so original equation

has no solution. [Ans]