If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? : GMAT Problem Solving (PS)
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# If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

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17 Dec 2012, 08:12
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2
[Reveal] Spoiler: OA
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

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17 Dec 2012, 08:14
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2

$$\frac{4-x}{2+x}=x$$ --> $$4-x=x*(2+x)$$ --> $$4-x=2x+x^2$$ --> $$x^2+3x-4=0$$. As you can see there is no need to solve for x to answer the question.

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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

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17 Dec 2012, 08:21
Simplify by keeping all the terms on side.
The equation becomes:

(4-x) = x*(2+x)

Now, expand the RHS of the equation:
(4-x) = 2x+x^2

Now, you see you already have a prt of the solution, a +ve x^2, so now, you need to move the LHS of the equation to the RHS and equate to 0:

0 = 2x+x^2-4+x

Simplify this further by adding 2x and x and voila!

x^2+3x-4 = 0

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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

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12 Jul 2014, 21:46
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

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29 Aug 2015, 02:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?   [#permalink] 29 Aug 2015, 02:06
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