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

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Difficulty:   55% (hard)

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

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

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

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Joined: 11 Sep 2015
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Re: The values of x for which the expression above is NOT defined are  [#permalink]

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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
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Re: The values of x for which the expression above is NOT defined are  [#permalink]

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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

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The values of x for which the expression above is NOT defined are  [#permalink]

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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  V
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Re: The values of x for which the expression above is NOT defined are  [#permalink]

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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! _________________
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Joined: 21 Feb 2017
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Re: The values of x for which the expression above is NOT defined are  [#permalink]

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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

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