Question

How do you solve the equation and identify any extraneous solutions for `x/(x-3) - 3/2 = 3/(x-3)`?

Answer 1

Add `3/2` to both sides to get:

`x/(x-3)=3/(x-3)+3/2`

Subtract `3/(x-3)` from both sides to get:

`3/2 = x/(x-3)-3/(x-3) = (x-3)/(x-3) = 1` with exclusion `x != 3`

This is false, so the equation has no solutions.