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If x#2, then (3x^2(x-2)-x+2)/(x-2)=

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New post 06 Mar 2014, 03:03
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(x \neq 2\), then \(\frac{3x^2(x-2)-x+2}{x-2}\)

(A) 3x^2 - x + 2
(B) 3x^2 + 1
(C) 3x^2
(D) 3x^2 - 1
(E) 3x^2 - 2

Problem Solving
Question: 133
Category: Algebra Simplifying algebraic expressions
Page: 79
Difficulty: 600


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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 06 Mar 2014, 03:03
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 06 Mar 2014, 03:08
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Factor out (x-2) which would get cancelled with the denominator, leaving us with 3x^2 - 1.

Answer (D).
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 06 Mar 2014, 04:05
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If x#2, then \(\frac{3x^2(x-2)-x+2}{x-2}\)

(A) 3x^2 - x + 2
(B) 3x^2 + 1
(C) 3x^2
(D) 3x^2 - 1
(E) 3x^2 - 2

Sol: The Given expression can be re-written as {3x^2 (x-2) -1 (x-2)}/(x-2)
Or Taking (x-2) common in the numerator we get ({3x^2-1)(x-2)}/(x-2)

Cancelling out (x-2), we get 3x^2-1

Ans is D
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 06 Mar 2014, 19:54
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(D) \(3x^2 - 1\)

Only one step required to get the answer:
Re-write equation as

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

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

= \(3x^2-1\)
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 08 Mar 2014, 12:50
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 14 Mar 2014, 04:35
Pick Numbers:

x = 4

3*4² (4-2)-4+2 / 4 - 2 = ...solve = 47, 47 = 3*4²-1. Hence D.
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 02 Mar 2015, 13:29
PareshGmat wrote:
(D) \(3x^2 - 1\)

Only one step required to get the answer:
Re-write equation as

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

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

= \(3x^2-1\)


Where does the "1" come from, why isnt it 3x^2(x-2) - x + 2 / x - 2 -> remove x -2 in the denominator and you get 3x^2 - x + 2?
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 02 Mar 2015, 14:46
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Hi erikvm,

The GMAT will frequently test you on rules that you know, but in ways that you're not used to thinking about....

Consider these examples:

Can you simplify 4X/4? What 'step' do you do?

Next, can you simplify (4X + 6)/2? What 'steps' do you do here?

The same rules apply to the question here. You have to divide the ENTIRE numerator by the denominator.

As it stands, this question can be solved rather easily by TESTing VALUES. Try using X = 3 and see how long it takes to get to the correct answer....

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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 03 Mar 2015, 04:20
Thanks Rich, you always manage to explain things in a very simple way.
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 21 Feb 2016, 14:15
Hi Abhinav,

You CAN get to the correct answer by TESTing VALUES and using X=1. However, I think that you made a mistake in your calculation at some point. Answer B does NOT match up with the value of that equation when you use X=1.

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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 15 Mar 2016, 14:14
I don't get why you distribute the "-" into the "2" with no parentheses around the last two terms. I can understand distributing if it read "-(x+2)" but it reads "-x+2." Am I losing my mind?
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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 27 Apr 2017, 21:35
This question seems easy (I got it wrong btw), but it's tricky if you don't see the "-1", so I will write it all out here for those who are struggling to see it.

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

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Re: If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 29 May 2017, 21:57
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If \(x \neq 2\), then \(\frac{3x^2(x-2)-x+2}{x-2}\)

(A) 3x^2 - x + 2
(B) 3x^2 + 1
(C) 3x^2
(D) 3x^2 - 1
(E) 3x^2 - 2

Problem Solving
Question: 133
Category: Algebra Simplifying algebraic expressions
Page: 79
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


First realize that x-2 appears in all three terms, albeit in an unfamiliar format in -x+2

To convert -x+2 to x-2, pull out the -1 from both x and -2: -1*(x-2).

Now the -1 already appears in the bar, so you can just put x-2 in parentheses to indicate that the -1 should be distributed.

3x^2*(x-2) -(x-2)/(x-2)

Divide out x-2 from all terms

3x^2 - 1.
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If x#2, then (3x^2(x-2)-x+2)/(x-2)=  [#permalink]

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New post 10 Mar 2018, 06:42
Bunuel wrote:
SOLUTION

If x#2, then \(\frac{3x^2(x-2)-x+2}{x-2}\)

(A) 3x^2 - x + 2
(B) 3x^2 + 1
(C) 3x^2
(D) 3x^2 - 1
(E) 3x^2 - 2

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

\(\frac{3x^2(x-2)-(x-2)}{x-2}\);

Reduce by x-2: \(3x^2 - 1\).

Answer: D.



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

\(\frac{3x^2 - x^2+2x+2}{x-2}\) I get this by multiplying -x by (x-2)

\(3x^2-x+2x\)

\(3x^2+x\)

so where am i wrong ?
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