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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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New post 17 Dec 2012, 09:12
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A
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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
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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, 09:14
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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, 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.
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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, 09:04
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, 15:46
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]

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New post 12 Mar 2018, 10:28
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



guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? :?
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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 12 Mar 2018, 11:59
dave13 wrote:
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



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


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.
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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 13 Mar 2018, 00:56
Gladiator59 wrote:
dave13 wrote:
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



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


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.



hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ? :)
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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 13 Mar 2018, 01:10
1
dave13 wrote:

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


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
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Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? &nbs [#permalink] 13 Mar 2018, 01:10
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