19 BBY, the Galactic Republic spots General Grievous in Utapau, the Separatists' Council Base; the Jedi Obi-Wan Kenobi is sent there to deal with him.
After a long search, Obi-Wan comes face to face with the Supreme Commander:
Obi-Wan: Surrender, it's over!
Grievous: Mwhahaha, fool! How can you beat me?!?!
Obi-Wan: With my lightsaber, of course!
Grievous: Mwhahaha, have you ever seen my set of four lightsabers?
Obi-Wan: Do you feel advantaged? May the math be with you! There's no difference between one and four!
Grievous: Can you prove it?
Obi-Wan:
$x=4$
$x(x-1)=4(x-1)$
$x^2-x=4x-4$
$x^2-4x=x-4$
$x(x-4)=x-4$
$x=1$
Grievous: You're trying to use the Force on me, but it won't work!
Is Obi-Wan's math as strong as his Force? Explain it!
If you like problems like this, check A dollar, a penny, there's no difference
Answer
When you multiplied both sides by $(x-1)$, you introduced the new extraneous solution $x=1$ to the equation. Later on when you divided by $(x-4)$, you forgot to case check that $(x-4)$ might equal $0$. If we do so we get $x = 1$ or $4$, as expected.
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