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

Question

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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lacktutor · Accepted Answer

\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.

nick1816 · Answer

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

GMATWhizTeam · Answer

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) (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.

sambitspm · Answer

(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

NitishJain · Answer

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.

shivani1351 · Answer

For this question, you should be aware of the following identities. If you know these, then this question is a super-easy one for you!

(a3+b3) = (a+b)(a2+b2-ab)
(a3-b3) = (a-b)(a2+b2+ab)
(a2-b2) = (a+b)(a-b)

Thus, 
(x3+1)(x3-1)/(x2-1) = (x+1)(x2+1-x)(x-1)(x2+1+x)/(x+1)(x-1)

(x2+1-x)(x2+1+x) = (x2+1)2 - (x2)

=> x^4+1+2x2-x2 = x^4+1+x2

Hence, the correct option is Option (A) (Answer)

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards