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Which of the following is equivalent to (2x+4)/[2x^2+8x+8]

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Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 06 Jun 2017, 01:39
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Which of the following is equivalent to \(\frac{(2x+4)}{[2x^2+8x+8]}\) for all values of x for which both expressions are defined?

A) 1/(2x^2+6)
B) 1/(9x+2)
C) 2/(x+6)
D) 1/(x+4)
E) 1/(x+2)

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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 06 Jun 2017, 02:28
GMATinsight wrote:
Which of the following is equivalent to \(\frac{(2x+4)}{[2x^2+8x+8]}\) for all values of x for which both expressions are defined?

A) 1/(2x^2+6)
B) 1/(9x+2)
C) 2/(x+6)
D) 1/(x+4)
E) 1/(x+2)


\(\frac{(2x+4)}{[2x^2+8x+8]}\) = \(\frac{2(x+2)}{2[x^2+4x+4]}\) = \(\frac{2(x+2)}{2(x+2)^2}\) = \(\frac{1}{(x+2)}\) . Answer E...
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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 06 Jun 2017, 10:02
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GMATinsight wrote:
Which of the following is equivalent to \(\frac{(2x+4)}{[2x^2+8x+8]}\) for all values of x for which both expressions are defined?

A) 1/(2x² + 6)
B) 1/(9x + 2)
C) 2/(x + 6)
D) 1/(x + 4)
E) 1/(x + 2)


sashiim20 has demonstrated the best/faster approach, BUT if you didn't think of that technique, you can still solve the question.
We're looking for an expression that is EQUIVALENT to (2x + 4)/(2x² + 8x + 8)
So, for ANY value of x, the correct answer must evaluate to have the same value as (2x + 4)/(2x² + 8x + 8) does

So, let's plug in a value for x
Let's try x = 1
First plug this value into the GIVEN expression.
We get: (2x + 4)/(2x² + 8x + 8) = [2(1) + 4]/[2(1²) + 8(1) + 8]
= 6/18
= 1/3

So, the correct answer choice will be the one that evaluates to 1/3 when we plug in x = 1
A) 1/(2x² + 6) = 1/[2(1²) + 6] = 1/8. We want 1/3, so ELIMINATE A
B) 1/(9x + 2) = 1/[9(1) + 2] = 1/11. We want 1/3, so ELIMINATE B
C) 2/(x + 6) = 2/(1 + 6) = 2/7. We want 1/3, so ELIMINATE C
D) 1/(x + 4) = 1/(1 + 4) = 1/5. We want 1/3, so ELIMINATE D
E) 1/(x + 2) = 1/(1 + 2) = 1/3. BINGO!!

By the process of elimination, the correct answer is

Cheers,
Brent

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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 08 Jun 2017, 16:47
GMATinsight wrote:
Which of the following is equivalent to \(\frac{(2x+4)}{[2x^2+8x+8]}\) for all values of x for which both expressions are defined?

A) 1/(2x^2+6)
B) 1/(9x+2)
C) 2/(x+6)
D) 1/(x+4)
E) 1/(x+2)


We can simplify the given equation:

(2x + 4)/(2x^2 + 8x + 8)

2(x + 2)/2(x^2 + 4x + 4)

(x + 2)/(x^2 + 4x + 4)

(x + 2)/[(x + 2)(x + 2)]

1/(x + 2)

Answer: E
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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 19 Nov 2019, 06:45
What about the mod sign in the denominator??
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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]  [#permalink]

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New post 19 Nov 2019, 11:21
devavrat wrote:
What about the mod sign in the denominator??


devavrat , its not mod sign , the user intends to mean brackets....
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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]   [#permalink] 19 Nov 2019, 11:21
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