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555-605 Level|   Algebra|      
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Bunuel
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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 10 Jun 2025, 00:30
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C
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25% (medium)

Question Stats:

74% (01:29) correct 26% (02:26) wrong based on 103 sessions

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If x^2 ≠ 1, which is equal to \(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}\)?

A. \(\frac{(−x + 3)}{(x + 1)}\)

B. \(\frac{2}{(x + 1)}\)

C. \(\frac{−2}{(x + 1)}\)

D. \(\frac{2}{(x − 1)}\)

E. \(\frac{−2}{(x − 1)}\)


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C
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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 10 Jun 2025, 02:33
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x/(x+1) - x/(x-1) +2/(x^2 -1)
Taking LCM
(x(x-1) -x(x+1)+2)/(x^2-1)
(x^2 -x -x^2 -x+2)/(x+1)(x-1)
(-2x+2)/(x+1)(x-1)
(-2)(x-1)/(x+1)(x-1)
-2/(x+1)

Answer: C
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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 10 Jun 2025, 09:46
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If x^2 ≠ 1, which is equal to \(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}\)?

A. \(\frac{(−x + 3)}{(x + 1)}\)

B. \(\frac{2}{(x + 1)}\)

C. \(\frac{−2}{(x + 1)}\)

D. \(\frac{2}{(x − 1)}\)

E. \(\frac{−2}{(x − 1)}\)


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\(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}\)

Taking the LCM as (x^2 -1) = (x-1)*(x+1)


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

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

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

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

Option C
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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 10 Jun 2025, 23:58
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\(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}\)
\(\frac{x(x-1)-x(x+1)}{(x+1)(x − 1)} + \frac{2}{(x^2 − 1)}\)
\(\frac{x^2-x-x^2-x}{(x^2 − 1)} + \frac{2}{(x^2 − 1)}\)
\(\frac{-2x+2}{(x^2 − 1)}\)
\(\frac{-2(x-1)}{(x+1)(x-1)}\)
\(\frac{-2}{(x+1)}\)

Bunuel
If x^2 ≠ 1, which is equal to \(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}\)?

A. \(\frac{(−x + 3)}{(x + 1)}\)

B. \(\frac{2}{(x + 1)}\)

C. \(\frac{−2}{(x + 1)}\)

D. \(\frac{2}{(x − 1)}\)

E. \(\frac{−2}{(x − 1)}\)


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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 21 Jun 2025, 10:22
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[ltr]Given

[/ltr]
simplifying by cross multiplying first terms gives
[x(x-1) - x(x+1)]/[x^2 - 1] + 2/(x^2 - 1)

Solving we get

-2(x-1)/(x^2 - 1)

Simplifying we get

-2/(x+1) Option C
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If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ? 23 Jun 2025, 23:19
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mentioning Bunuel for checking

x^2 is not equal to 1
which means x>1

assume x = 2

2/2+1 - 2/1 + 2/2^2-1

2/3 - 2 + 2/3

4/3 - 2

-2/3

we know 3 = x + 1

thus -2/ x + 1

is it the correct approach to this question?
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