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Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for

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Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for  [#permalink]

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New post 20 Aug 2018, 22:52
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:45) correct 14% (02:32) wrong based on 48 sessions

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Re: Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for  [#permalink]

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New post 20 Aug 2018, 23:13
Bunuel wrote:
Which of the following is equivalent to \(\frac{2x^2+8x−24}{2x^2+20x−48}\) for all values of x for which both expressions are defined?


A. (x−2)/(x−4)

B. (x−2)/(x+4)

C. (x+2)/(x+4)

D. (x+2)/(x−12)

E. (x+6)/(x+12)


\(\frac{2x^2+8x−24}{2x^2+20x−48}\)
=\(\frac{2(x^2+4x−12}{2(x^2+10x−24)}\)
=\(\frac{x^2+6x-2x−12}{x^2+12x-2x−24}\)
=\(\frac{x(x+6)-2(x+6)}{x(x+12)-2(x+12)}\)
=\(\frac{(x+6)(x-2)}{(x+12)(x-2)}\)
=\(\frac{(x+6)}{(x+12)}\)

Ans. (E)
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Re: Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for  [#permalink]

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New post 20 Aug 2018, 23:47
Factorizing both numerator and denominator gives
\(\frac{{2x^2+12x-4x-24}}{{2x^2+24x-4x-48}}\)

\(\frac{{(2x-4)(x+6)}}{{(2x-4)(x+12)}}\)

We get,

\(\frac{{(x+6)}}{{(x+12)}}\)

E is the answer.
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Re: Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for   [#permalink] 20 Aug 2018, 23:47
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