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 Post subject: GMAT AlgebraPosted: Sat Aug 06, 2011 12:46 pm

Joined: Sat Aug 06, 2011 12:40 pm
Posts: 2
Does this equation have a solution?
(x² – 4x + 4)/(x – 2)=0

If you solve for the numerator, you get x = 2, which when plugged into the denominator makes 2 – 2 = 0, making the equation UNSOLVABLE.

However, if you divide the binomial into (x + 2)(x – 2)/(x – 2)=0, then wouldn't you cancel out the matching (x – 2)s in the numerator and denominator, leaving you with (x + 2) = 0...making the solution x = -2?

The solution given by 800score is x = 2. Please explain!

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 Post subject: Re: Algebra Section 2: "Very Sneaky Unsolvable Equations"Posted: Thu Aug 11, 2011 5:51 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Note, that you refer to the previous version of the prep guide. I'd like to let you know that there is a newer version on the website now.
As always we keep on improving, to deliver the best and most up-to-date experience.

Here is the answer to your question.
There are two different problems mentioned in your inquiry.
Quote:
Does this equation have a solution?
(x² – 4x + 4)/(x – 2) = 0
As it had been written in the prep guide, the numerator can be transformed into (x – 2)². It equals 0 only if x = 2. But the denominator would be 0, if x = 2. Division by 0 is undefined, so the equation has NO solution.
The WRONG way to solve was also provided in the prep guide, so that a student could see the trap. Apparently, you thought of it as of the proper one.

Quote:
However, if you divide the binomial into (x + 2)(x – 2)/(x – 2) = 0, then wouldn't you cancel out the matching (x – 2)s in the numerator and denominator, leaving you with (x + 2) = 0...making the solution x = -2?
This equation is (x² – 4)/(x – 2) = 0. Note, that it differs from the previous one.
The numerator, (x + 2)(x – 2), equals 0 when x = -2 or x = 2. However x = 2 does not fit in the original equation, since the denominator must NOT equal 0. So x = -2 is the only solution.

Note, that you can cancel out same expression, assuming it does not equal 0, but keep in mind the "prohibited" value of x, which turnes this expression into 0. Or you can plug all the solutions into the original equation to see if all the denominators are Ok.

P.S. In different types of the questions, when you do not solve an equation but you are asked to simplify a formula, it is assumed that all the denominators are Ok.

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 Post subject: Re: Algebra Section 2: "Very Sneaky Unsolvable Equations"Posted: Wed Aug 24, 2011 12:19 pm

Joined: Sat Aug 06, 2011 12:40 pm
Posts: 2
Thank you for your help. I definitely understand the problem now, but you mentioned that there's a newer version of the prep guide available...can you please copy me the link to this? Because every time I sign on, it shows me this same version.
Thanks!

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 Post subject: Re: Algebra Section 2: "Very Sneaky Unsolvable Equations"Posted: Sun Aug 28, 2011 4:27 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
koperwbi wrote:
you mentioned that there's a newer version of the prep guide available...can you please copy me the link to this? Because every time I sign on, it shows me this same version.

You need to reload you browser or clear the browsing cache.

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