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555-605 (Medium)|   Algebra|      
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Bunuel
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(x - 2)/(x^2 - 4) = 1 which of the following can x be 17 Nov 2023, 02:30
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35% (medium)

Question Stats:

70% (00:56) correct 30% (01:10) wrong based on 84 sessions

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\(\frac{(x-2)}{(x^2-4)} =1 \) which of the following can x be?

A. -1 and 2
B. -2
C. -3 and -1
D. -1
E. -2, -1 and 2

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D
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Mizan42
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(x - 2)/(x^2 - 4) = 1 which of the following can x be 21 Nov 2023, 03:35
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Put directly -1,
Then calculate,
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IshanSaini
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(x - 2)/(x^2 - 4) = 1 which of the following can x be 21 Nov 2023, 12:07
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This is a tricky question.
Step 1. Simply solve the simple quadratic eqn.
Step 2. You will get x = 2 or -1.
Step 3. See that x^2 in denom will make x^2 -4 = 0 if x = 2.
Step 4. As per above logic, discard 2, we are only left with -1 hence imo D

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umang.lakhani
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(x - 2)/(x^2 - 4) = 1 which of the following can x be 22 Nov 2023, 08:03
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Can I open the denom with a^2 - b^2 = (a+b)*(a-b) and then cancel out x-2 from num and denom? Is this the right approach?
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Bunuel
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(x - 2)/(x^2 - 4) = 1 which of the following can x be 22 Nov 2023, 08:40
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umang.lakhani
\(\frac{x-2}{x^2-4} =1 \) which of the following can x be?

A. -1 and 2
B. -2
C. -3 and -1
D. -1
E. -2, -1 and 2

Can I open the denom with a^2 - b^2 = (a+b)*(a-b) and then cancel out x-2 from num and denom? Is this the right approach?
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Yes, that would be correct:

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

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

We can reduce by x - 2 here because it cannot be 0:

    \(\frac{1}{x+2} =1 \);

    \(1 = x+2\);

    \(x=-1\)
.

Answer: D.
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