Which of the following is equivalent to for all values of x for which : Problem Solving (PS)

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

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Math Expert

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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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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

Spoiler: OA

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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

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

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

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

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

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

\(2(x+1)\)

Answer: Option B
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Math Expert

Joined: 02 Aug 2009

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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, 08:25

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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Marshall & McDonough Moderator

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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.

Answer: B