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]

17 Dec 2012, 09:12

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Question Stats:

75% (01:30) correct

25% (01:27) wrong

based on 24 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

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

17 Dec 2012, 09:14

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]

17 Dec 2012, 09:21

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, 09:21

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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 ?

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

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