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I need some help with this rational equation. It's supposed to = -1, but for some strange reason I keep getting x^2 +2x = -1.


I don't know if that's the answer and I'm supposed to just listen to the "=-1" part or I'm just doing it completely wrong.


Anyways, here's the equation:


1) x/x-1 = 1/x+3

Verified Answer :

AL2006


This one is so easy that your brain refuses to accept it.
It's looking for a harder answer, but can't find it !

You're totally correct, as far you went.     x² + 2x does = -1

Now add ' 1 ' to each side:     x² + 2x + 1 = 0

Can you factor that quadratic ?
Can you mash it through the quadratic formula ?

Actually, it's the simplest possible perfect square.

                                       x² + 2x + 1  =  (x + 1)²

So the solutions of     x² + 2x + 1 = 0  are both   x = -1 .

Don't say anything.
I know it's embarrassing.

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