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# Which of the following is equivalent to for all values of x for which

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Math Expert
Joined: 02 Sep 2009
Posts: 46203
Which of the following is equivalent to for all values of x for which [#permalink]

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15 Jan 2018, 06:18
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Difficulty:

45% (medium)

Question Stats:

62% (02:34) correct 38% (01:42) wrong based on 29 sessions

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Which of the following is equivalent to for all values of x for which both $$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}$$ expressions are defined?

(A) 2x^2 - 2
(B) 2x + 2
(C) x + 1
(D) 2x + 6
(E) x - 1

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Re: Which of the following is equivalent to for all values of x for which [#permalink]

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15 Jan 2018, 08:21
Bunuel wrote:
Which of the following is equivalent to for all values of x for which both $$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}$$ expressions are defined?

(A) 2x^2 - 2
(B) 2x + 2
(C) x + 1
(D) 2x + 6
(E) x - 1

$$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}$$

$$\frac{(2x^2-2)(x + 3)}{(x+3)*(x-1)}$$

$$\frac{(2x^2-2)}{(x-1)}$$

$$\frac{2(x^2-1)}{(x-1)}$$

$$\frac{2(x-1)(x+1)}{(x-1)}$$

$$2(x+1)$$

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Math Expert
Joined: 02 Aug 2009
Posts: 5893
Re: Which of the following is equivalent to for all values of x for which [#permalink]

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15 Jan 2018, 08:25
2
Bunuel wrote:
Which of the following is equivalent to for all values of x for which both $$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}$$ expressions are defined?

(A) 2x^2 - 2
(B) 2x + 2
(C) x + 1
(D) 2x + 6
(E) x - 1

Substitution is going to be the best way here, but pick up smart number..
x as 0 does not give us a denominator as 0 and also eases out calculations..
all terms with x will become 0..

$$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}=\frac{-6}{-3}=2$$

It is very clear looking at the choices, at first glance itself, that only B will leave 2 as answer
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Re: Which of the following is equivalent to for all values of x for which [#permalink]

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15 Jan 2018, 08:26
$$\frac{2x^2(x + 3) -2x -6}{x^2 + 2x - 3}$$

= $$\frac{2x^2(x + 3) - 2 (x + 3)}{x^2 + 3x - x - 3}$$

= $$\frac{2(x^2 - 1)(x + 3)}{(x + 3)(x - 1)}$$

= $$2(x + 1)$$

= 2x + 2

Alternate approach: Put x = 0 in the given equation, we get the value as 2. Substitute x = 0 in the options, only option B remains.

Re: Which of the following is equivalent to for all values of x for which   [#permalink] 15 Jan 2018, 08:26
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