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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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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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Walkabout wrote:
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.

Answer: C.
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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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New post 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

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

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Hello from the GMAT Club BumpBot!

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

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New post 23 May 2017, 08:04
Walkabout wrote:
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


\(\frac{(4 - x)}{(2 + x)} = x\)

Or, \(4 - x = 2x +x^2\)

Or, \(x^2 + 3x - 4 = 0\)

Thus, the answer must be (C) 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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New post 25 May 2017, 14:46
Walkabout wrote:
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


We can simplify the given equation by first multiplying each side of the equation by (2 + x).

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

4 - x = x(2 + x)

4 - x = x^2 + 2x

x^2 + 3x - 4 = 0

Answer: C
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?   [#permalink] 25 May 2017, 14:46
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