If x ≠ 2 and (x - 1)(x^2 + 1)/(x-2) = 0, then x =

Question

If x ≠ 2 and  \frac{(x - 1)(x^2 + 1)}{(x-2)} = 0 , then x =

A. -2
B. -1
C. 1
D. 2
E. 0

Luckisnoexcuse · Answer

For  \frac{(x - 1)(x^2 + 1)}{(x-2)} = 0 ,

either x-1 = 0 or (x^2 + 1) = 0

X=1

hence C

shashankism · Answer

\frac{(x - 1)(x^2 + 1)}{(x-2)} = 0 
Since x =/= 2

Also x^2 +1 >0

-> x-1 = 0 
-> x = 1

Answer C.

BrentGMATPrepNow · Answer

The above solutions are perfect. 
However, if your algebra skills aren't that strong, you can quickly solve this question by plugging in the answer choices to see which one satisfies the equation.

Given: (x - 1)(x² + 1)/(x-2) = 0

A.  -2 
Plug in to get: ( -2  - 1)(( -2 )² + 1)/( -2  - 2) = 0
Evaluate: 15/4 = 0
Doesn't work...ELIMINATE A

B.  -1 
Plug in to get: ( -1  - 1)(( -1 )² + 1)/( -1  - 2) = 0
Evaluate: 4/3 = 0
Doesn't work...ELIMINATE B

C.  1 
Plug in to get: ( 1  - 1)(( 1 )² + 1)/( 1  - 2) = 0
Evaluate: 0/(-1) = 0
WORKS!!

Answer:  C

Cheers,
Brent

Abhishek009 · Answer

\frac{(x - 1)(x^2 + 1)}{(x-2)} = 0

So, Either  (x - 1)  or  (x^2 + 1)  must be  0  , as  x - 2  can't be  0  , as anything divided by  0  will result in  ∞

If  x - 1 = 0  ,  x = 1  ( option C)

Thus, the correct answer must be (C) , you can check with  (x^2 + 1)  , the result will be same.

JeffTargetTestPrep · Answer

The only way for a fractional expression to equal zero is when the numerator is equal to zero. Thus, we can ignore the denominator and set the numerator equal to 0 to solve for x:
 
(x -1)(x^2 + 1) = 0
 
x = 1 
 
OR
 
x^2 +1 = 0
 
x^2 = -1
 
Notice that x^2 can never be negative, so x^2 can’t be equal to -1. So x = 1 is the only solution.
 
Answer: C

ydmuley · Answer

x ≠ 2 and  \frac{(x - 1)(x^2 + 1)}{(x-2)} = 0

Based on given information, we cannot make denominator to ZERO as  x != 2

So in order to make numerator ZERO we either have to make  (x - 1)  or  (x^2 + 1)  as ZERO.

As we can see that equation  (x^2 + 1)  will always be positive, so we are left with only one choice.

Making  (x - 1)  as ZERO and we can do that by take value of x as 1

Hence, Answer is C

bumpbot · Answer

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If x ≠ 2 and (x - 1)(x^2 + 1)/(x-2) = 0, then x =

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If x ≠ 2 and (x - 1)(x^2 + 1)/(x-2) = 0, then x =

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