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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] New post 17 Dec 2012, 08:12
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:54) correct 19% (01:11) wrong based on 101 sessions
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] New post 17 Dec 2012, 08:14
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink] 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.
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?   [#permalink] 17 Dec 2012, 08:21
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If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

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