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

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Math Expert
Joined: 02 Sep 2009
Posts: 49231
Which of the following is equivalent to (2x^2+8x−24)/(2x^2+20x−48) for  [#permalink]

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20 Aug 2018, 22:52
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Difficulty:

15% (low)

Question Stats:

84% (01:16) correct 16% (01:49) wrong based on 43 sessions

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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)

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

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