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If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to

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If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 06 Mar 2020, 02:17
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If \(x ≠ 1\) and \(x ≠ -1\), then \(\frac{(x^3 + 1)(x^3 − 1 )}{(x^2 − 1)}\) must equal to which of the folllowing?


A. \(x^4 + x^2 + 1\)

B. \(x^4 + x^3 + x + 1\)

C. \(x^6 – 1 \)

D. \(x^6 + 1\)

E. \(x^4 + x^2 - 1\)




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If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 06 Mar 2020, 02:41
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\(\frac{(x^3 + 1)(x^3 − 1 )}{(x^2 − 1)}=\frac{(x^{6}-1)}{ (x^{2}-1)}=\)

= \(\frac{(x^{2}-1)(x^{4}+ x^{2}+1)}{(x^{2}-1)}\)

\(x≠1\) and \(x≠-1\)
--> \(x^{4}+ x^{2}+1\)

The answer is A.
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Re: If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 06 Mar 2020, 02:53
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\(x^3+1= (x+1)(x^2-x+1)\)
\(x^3-1= (x-1)(x^2+x+1)\)
\(x^2-1=(x+1)(x-1)\)

Since, \(x^2≠1\)
\(\frac{(x^3 + 1)(x^3 − 1 )}{(x^2 − 1)}\)= \((x^2-x+1)*(x^2+x+1)= (x^2+1)^2 -x^2= x^4+x^2+1\)



Bunuel wrote:
If \(x ≠ 1\) and \(x ≠ -1\), then \(\frac{(x^3 + 1)(x^3 − 1 )}{(x^2 − 1)}\) must equal to which of the folllowing?


A. \(x^4 + x^2 + 1\)

B. \(x^4 + x^3 + x + 1\)

C. \(x^6 – 1 \)

D. \(x^6 + 1\)

E. \(x^4 + x^2 - 1\)




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Re: If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 06 Mar 2020, 04:26
1
1
Bunuel wrote:
If \(x ≠ 1\) and \(x ≠ -1\), then \(\frac{(x^3 + 1)(x^3 − 1 )}{(x^2 − 1)}\) must equal to which of the folllowing?


A. \(x^4 + x^2 + 1\)

B. \(x^4 + x^3 + x + 1\)

C. \(x^6 – 1 \)

D. \(x^6 + 1\)

E. \(x^4 + x^2 - 1\)




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Solution:


    • \((x^3 + 1) = (x + 1) (x^2 -x + 1) \)
    •\((x^3 - 1) = (x - 1) (x^2 + x + 1)\)
    •\((x^3 + 1)(x^3 - 1) = (x^2 - 1) [(x^2 + 1)^2 - x ^2] =(x^2 - 1) (x^4 + x^2 + 1)\)
    • \(\frac{(x^3 + 1)(x^3 - 1)}{(x^2- 1)} = \frac{(x^2 - 1) (x^4 + x^2 + 1)}{(x^2 - 1)}
    \)
After cancelling \((x^2 -1)\), we get
    • \(x^4 + x^2 + 1\)
Hence, the correct answer is Option A.
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Re: If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 30 May 2020, 05:26
(x^3+1)(x^3-1)/ (x^2-1)

Numerator x^3-1 = (x-1)(x^2+1+x)
Denominator = (x-1)(x+1)
Numerator x^3+1 = (x+1)(x^2+1-x)

Hence expression comes as
(x^2+x+1)(x^2-x+1)

(x^2+1)^2 -x^2
x^4+x^2+1

Hence A
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Re: If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to  [#permalink]

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New post 30 May 2020, 07:45
I wasn't aware of the formula, so i used substitution method; x=2

Putting x= 2 in given eqn, we get 21.

By putting 2 in all options, only A gives 21.
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Re: If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to   [#permalink] 30 May 2020, 07:45

If x ≠ 1 and x ≠ -1, then (x^3 + 1)(x^3 − 1 )/(x^2 − 1) must equal to

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