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If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16

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If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16 [#permalink]

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New post 11 Dec 2015, 08:49
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If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16) ?

A. (x + 4)/(4(x - 4))
B. (x - 4)/(x + 4)
C. (x - 2)/(x + 4)
D. (x + 4)/(x - 4)
E. (x - 8)/(x - 4)

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Re: If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16 [#permalink]

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New post 12 Dec 2015, 14:44
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Bunuel wrote:
If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16) ?

A. (x + 4)/(4(x - 4))
B. (x - 4)/(x + 4)
C. (x - 2)/(x + 4)
D. (x + 4)/(x - 4)
E. (x - 8)/(x - 4)


Some readers might be wondering why Bunuel added the part about x > 7.
This is to make the simplification of x^2 + 8x + 16)/(x^2 - 16) mathematically sound.
When we factor this we get (x + 4)(x + 4)/(x + 4)(x - 4)
However, we can't automatically eliminate (x + 4) from top and bottom to conclude that (x + 4)(x + 4)/(x + 4)(x - 4) = (x + 4)/(x - 4)
Why not?
Well, we must first ensure that x does not equal -4.
If x = -4, then (x + 4) = 0, so we are essentially dividing top and bottom by 0, which is not cool.
To avoid this situation, Bunuel stated that x > 7, which means x CANNOT equal -4.

For more on this (and on simplifying algebraic fractions), see our free video - http://www.gmatprepnow.com/module/gmat- ... /video/958

Cheers,
Brent
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Re: If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16 [#permalink]

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New post 11 Dec 2015, 14:48
IMO 'D' is the answer.
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If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16 [#permalink]

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New post 12 Dec 2015, 14:26
(x^2 + 8x + 16)/(x^2 - 16)
= (x + 4)(x + 4) / (x + 4)(x - 4)
=(x + 4)/(x - 4)

D. (x + 4)/(x - 4)
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Re: If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16 [#permalink]

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New post 27 Nov 2017, 12:28
Bunuel wrote:
If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16) ?

A. (x + 4)/(4(x - 4))
B. (x - 4)/(x + 4)
C. (x - 2)/(x + 4)
D. (x + 4)/(x - 4)
E. (x - 8)/(x - 4)


Let’s simplify the given equation:

(x^2 + 8x + 16)/(x^2 - 16)

(x + 4)(x + 4)/[(x - 4)(x + 4)]

(x + 4)/(x - 4)

Answer: D
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Re: If x > 7, which of the following is equal to (x^2 + 8x + 16)/(x^2 - 16   [#permalink] 27 Nov 2017, 12:28
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