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Re: Which of the following is equivalent to (2x+4)/[2x^2+8x+8]
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06 Jun 2017, 09:02
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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