GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Aug 2020, 02:39

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

The values of x for which the expression above is NOT defined are

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65829
The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

22 May 2020, 06:53
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:12) correct 47% (01:24) wrong based on 150 sessions

HideShow timer Statistics

$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

The values of x for which the expression above is NOT defined are

A. 1 and 2 only
B. –1 and 2 only
C. –1 and –2 only
D. –1, 1, and –2
E. –1, 1, and 2

PS21172

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4999
GMAT 1: 770 Q49 V46
Re: The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

22 May 2020, 07:11
1
Top Contributor
2
Bunuel wrote:
$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

The values of x for which the expression above is NOT defined are

A. 1 and 2 only
B. –1 and 2 only
C. –1 and –2 only
D. –1, 1, and –2
E. –1, 1, and 2

PS21172

Key concept: A rational expression (aka fraction) is undefined when the denominator equal zero

So let's check each denominator individually and see what values of x make that denominator equal to zero.

If $$x^2 - 1 = 0$$, then $$x^2 = 1$$, which means $$x=1$$ and $$x=-1$$
In other words, the expression is not defined when $$x=1$$ and when $$x=-1$$

If $$x^2 - 4x + 4 = 0$$, then we can factor the left side to get: $$(x-2)(x-2)= 0$$
This means $$x = 2$$
So, the expression is not defined when $$x=2$$

So the expression is undefined when $$x=1$$, $$x=-1$$ and $$x=2$$

Cheers,
Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.

General Discussion
GMAT Club Legend
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A motivator and an Optimist :)
Joined: 08 Jul 2010
Posts: 4521
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

22 May 2020, 08:25
Bunuel wrote:
$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

The values of x for which the expression above is NOT defined are

A. 1 and 2 only
B. –1 and 2 only
C. –1 and –2 only
D. –1, 1, and –2
E. –1, 1, and 2

PS21172

CONCEPT: an expression is NOT DEFINED when denominator = 0

i.e. in the expression $$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

$$x^2 - 1 = 0$$ i.e. x = +1 or -1
and
$$x^2 - 4x + 4 = 0$$ i.e $$(x -2)^2 = 0$$ i.e. x = 2

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Director
Joined: 21 Feb 2017
Posts: 677
GMAT 1: 690 Q45 V38
The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

15 Jun 2020, 04:09
GMATinsight

$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

if i solve this further i get

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

cancelling like terms

$$\frac{1}{x-1} - \frac{1}{x-2}$$

now the only values that give denominator 0 are 1 and 2
i know im missing -1 here, but could you help with where I went wrong? which term did I cancel that I wasn't supposed to cancel and why?
GMAT Club Legend
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A motivator and an Optimist :)
Joined: 08 Jul 2010
Posts: 4521
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

15 Jun 2020, 04:40
Kritisood wrote:
GMATinsight

$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

if i solve this further i get

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

cancelling like terms

$$\frac{1}{x-1} - \frac{1}{x-2}$$

now the only values that give denominator 0 are 1 and 2
i know im missing -1 here, but could you help with where I went wrong? which term did I cancel that I wasn't supposed to cancel and why?

Kritisood

Canceling Like terms is acceptable ONLY

- If the term to be canceled is NON-ZERO

You are canceling the term (x+1) without knowing whether it's NON-ZERO - $$This is the mistake$$

Since that term also may be 0 bring the situation of $$\frac{0}{0}$$ therefore it will be WRONG to cancel it.

SImilar example
$$x^2-2x = 0$$ does NOT mean $$x*x = 2x$$ and $$x = 2$$
$$x^2-2x = 0$$ means $$x*(x-2) = 0$$ i.e. x = 0 or 2

I hope this help!
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Director
Joined: 21 Feb 2017
Posts: 677
GMAT 1: 690 Q45 V38
Re: The values of x for which the expression above is NOT defined are  [#permalink]

Show Tags

15 Jun 2020, 06:35
GMATinsight wrote:
Kritisood wrote:
GMATinsight

$$\frac{x + 1}{x^2 - 1} - \frac{x - 2}{x^2 - 4x + 4}$$

if i solve this further i get

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

cancelling like terms

$$\frac{1}{x-1} - \frac{1}{x-2}$$

now the only values that give denominator 0 are 1 and 2
i know im missing -1 here, but could you help with where I went wrong? which term did I cancel that I wasn't supposed to cancel and why?

Kritisood

Canceling Like terms is acceptable ONLY

- If the term to be canceled is NON-ZERO

You are canceling the term (x+1) without knowing whether it's NON-ZERO - $$This is the mistake$$

Since that term also may be 0 bring the situation of $$\frac{0}{0}$$ therefore it will be WRONG to cancel it.

SImilar example
$$x^2-2x = 0$$ does NOT mean $$x*x = 2x$$ and $$x = 2$$
$$x^2-2x = 0$$ means $$x*(x-2) = 0$$ i.e. x = 0 or 2

I hope this help!

This helps a lot, thank you so much GMATinsight
Re: The values of x for which the expression above is NOT defined are   [#permalink] 15 Jun 2020, 06:35