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

Question

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

Bunuel · Accepted Answer

\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.

karanamin · Answer

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.

GMATinsight · Answer

To solve any such question, I suggest that one should try to find one possible value of x that satisfies the given expression (4-x)/(2+x)=x

Try substituting Integer values in the range {-3, -2, -1, 0, 1, 2, 3}

The value x=1 satisfies the expression (4-x)/(2+x)=x

Hence, @x=1, x^2+3x-4 = 1^2+3*1-4 = 0

Answer: Option C

JeffTargetTestPrep · Answer

We start by simplifying the given equation, (4-x)/(2+x) = x. We first multiply both sides by 2+x. Thus we have:

4 – x = x(2 + x)

4 – x = 2x + x^2

4 = 3x + x^2

x^2 + 3x – 4 = 0

Before moving any further we note that we are not being asked for the value of x but rather  the value of x^2 + 3x – 4 .

So see that x^2 + 3x – 4 = 0.

The answer is C.

Abhishek009 · Answer

\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

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

Given: (4 - x)/(2 + x) = x
Eliminate the fraction by multiplying both sides by (2 + x) to get: (4 - x) = (x)(2 + x)
Expand: 4 - x = 2x + x²
Add x to both sides: 4 = x² + 3x
Subtract 4 from both sides:  0  = x² + 3x - 4

PERFECT! The question asks us to find the value of x² + 3x - 4, and we just showed that the expression equals  0

Answer:  C

dave13 · Answer

guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ?

Gladiator59 · Answer

Not quite.

On solving the given equation ,

(4-x)/(2+x) = x 
 4-x = x*(2+x) 
 4-x = x^2 + 2x 
 0 = x^2 + 3x - 4

Hence 0.

dave13 · Answer

hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ?

Gladiator59 · Answer

Yeah  dave13 ,

Precisely so. "Quadratics" may or may not equal 0. What does always equal zero is a "Quadratic equation".

So for example.

x^2 +3x - 4 = 0  could be re-written as 
 x^2 + 3x -3 = 1  ( adding 1 to both RHS and LHS )

Here the LHS is a "quadratic" expression that equals 1 (RHS)

More generally speaking .. quadratic expressions are parabolas and where the intersect the x-axis they  equal zero .

Best,
Gladi

Kinshook · Answer

4-x = 2x + x^2
x^2+3x-4=0

IMO C

Posted from my mobile device

Abhishek009 · Answer

4 - x = 2x + x^2

So,  x^2 + 3x - 4 = 0 , Answer will be (C)

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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 ?

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