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

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

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New post 24 May 2019, 02:20
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[GMAT math practice question]

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

\(A. 0\)

\(B. 1\)

\(C. 2\)

\(D. 3\)

\(E. 4\)

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

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New post 24 May 2019, 02:32
X is never equal to X-1 so, zero roots.

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

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New post 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
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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New post 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
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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New post 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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New post 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.

Thanks in advance.
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Re: How many roots does the equation (x^2-1)/(x+1)=x have?  [#permalink]

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New post 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.

Thanks in advance.


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

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New post 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

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