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# How many roots does the equation (x^2-1)/(x+1)=x have?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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24 May 2019, 02:20
1
2
00:00

Difficulty:

45% (medium)

Question Stats:

50% (00:49) correct 50% (00:53) wrong based on 82 sessions

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[GMAT math practice question]

How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have?

$$A. 0$$

$$B. 1$$

$$C. 2$$

$$D. 3$$

$$E. 4$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 22 Jan 2019 Posts: 3 Re: How many roots does the equation (x^2-1)/(x+1)=x have? [#permalink] ### Show Tags 24 May 2019, 02:32 X is never equal to X-1 so, zero roots. Posted from my mobile device GMAT Club Legend Joined: 18 Aug 2017 Posts: 5428 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: How many roots does the equation (x^2-1)/(x+1)=x have? [#permalink] ### Show Tags 24 May 2019, 09:28 MathRevolution wrote: [GMAT math practice question] How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have? $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. 4$$ solve for $$\frac{(x^2-1)}{(x+1)}=x$$ we get x-1=x x=0 roots IMO A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8231 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many roots does the equation (x^2-1)/(x+1)=x have? [#permalink] ### Show Tags 26 May 2019, 18:58 => $$\frac{(x^2-1)}{(x+1)}=x$$ $$=> \frac{(x+1)(x-1)}{(x+1)} = x$$ $$=> x-1 = x$$ by canceling $$(x+1).$$ But $$x – 1 = x$$ has no solution. Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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26 May 2019, 19:02
MathRevolution wrote:
[GMAT math practice question]

How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have?

$$A. 0$$

$$B. 1$$

$$C. 2$$

$$D. 3$$

$$E. 4$$

Cross multiply:- x^2 -1 = x^2 + x
x= -1, one root but not possible as it'll render the LHS infinity. So zero root. (A)
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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03 Jun 2019, 12:35
LeoN88 wrote:
MathRevolution wrote:
[GMAT math practice question]

How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have?

$$A. 0$$

$$B. 1$$

$$C. 2$$

$$D. 3$$

$$E. 4$$

Cross multiply:- x^2 -1 = x^2 + x
x= -1, one root but not possible as it'll render the LHS infinity. So zero root. (A)

LeoN88,
Can you please explain the portion marked by green-

Cross multiply:- x^2 -1 = x^2 + x
x= -1, one root but not possible as it'll render the LHS infinity. So zero root.

ISB School Moderator
Joined: 08 Dec 2013
Posts: 615
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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03 Jun 2019, 17:28
1
tamal99 wrote:
LeoN88 wrote:
MathRevolution wrote:
[GMAT math practice question]

How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have?

$$A. 0$$

$$B. 1$$

$$C. 2$$

$$D. 3$$

$$E. 4$$

Cross multiply:- x^2 -1 = x^2 + x
x= -1, one root but not possible as it'll render the LHS infinity. So zero root. (A)

LeoN88,
Can you please explain the portion marked by green-

Cross multiply:- x^2 -1 = x^2 + x
x= -1, one root but not possible as it'll render the LHS infinity. So zero root.

tamal99

If I put x=-1 in the equation stem the denominator of the fraction will become infinity so not possible.

(x^2 -1 )/(x+1) so x!= -1
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GMAT 1: 640 Q50 V26
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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03 Jun 2019, 17:37
MathRevolution wrote:
[GMAT math practice question]

How many roots does the equation $$\frac{(x^2-1)}{(x+1)}=x$$ have?

$$A. 0$$

$$B. 1$$

$$C. 2$$

$$D. 3$$

$$E. 4$$

On solving the equation we get x = -1. But x = -1 cannot be the root. So we have 0 roots. So option A is correct

Posted from my mobile device
Re: How many roots does the equation (x^2-1)/(x+1)=x have?   [#permalink] 03 Jun 2019, 17:37
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