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

Question

If  x 
eq 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

Bunuel · Accepted Answer

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.

PareshGmat · Answer

(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

Donnie84 · Answer

Factor out (x-2) which would get cancelled with the denominator, leaving us with 3x^2 - 1.

Answer (D).

WoundedTiger · Answer

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

erikvm · Answer

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?

EMPOWERgmatRichC · Answer

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....

GMAT assassins aren't born, they're made,
Rich

erikvm · Answer

Thanks Rich, you always manage to explain things in a very simple way.

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

halfrican88 · Answer

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?

Bunuel · Answer

Notice that  -x+2 = -(x-2) .

diegocml · Answer

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

OA  D

mbaapp1234 · Answer

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.

MathRevolution · Answer

\frac{ }{ (x - 2)} = \frac{ }{ (x - 2)} = \frac{(x - 2) }{ (x - 2)}

=> (3 x^2  - 1)

Answer D

Abhishek009 · Answer

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

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

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

=  (3x^2 - 1) , Answer must be (D)

BrentGMATPrepNow · Answer

STRATEGY : Upon reading any GMAT Problem Solving question, we should always ask,   Can I use the answer choices to my advantage?   
In this case, we can easily test the answer choices for equivalency. 
Now let's give ourselves up to 20 seconds to identify a faster approach. 
In this case, we can also try to simplify the expression so that it matches one of the answer choices.
I think testing for equivalency will be faster, so I'll go with that...

Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x. 
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x. 
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 =  35 , and the expression 5x = 5(7) =  35

Let's test an easy value like  x = 0 . 
Plug  x = 0  into the given expression to get:  \frac{3x^2(x-2)-x+2}{x-2}=\frac{3(0)^2(0-2)-0+2}{0-2} = \frac{2}{-2}= -1

Now we'll plug  x = 0  into the five answer choices see which one(s) evaluate(s) to  -1

(A)  3(0)^2 - 0 + 2 = 2 . ELIMINATE

(B)  3(0)^2 + 1 = 1 . ELIMINATE

(C)  3(0)^2 = 0 . ELIMINATE

(D)  3(0)^2 - 1 = -1    GREAT! Keep.

(E)  3(0)^2 - 2 = -2 . ELIMINATE

Answer: D

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

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