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20 Apr 2017, 23:19
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C
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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. \(\frac{−2}{(x − 1)}\)
A. \(\frac{(−x + 3)}{(x + 1)}\)
B. \(\frac{2}{(x + 1)}\)
C. \(\frac{−2}{(x + 1)}\)
D. \(\frac{2}{(x − 1)}\)
E. \(\frac{−2}{(x − 1)}\)
21 Apr 2017, 01:53
Kudos
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x/x+1 - x/x-1 + 2/(x^2 -1)
Above can be written as
==> [x(x-1)/(x^2 -1] - [x(x+1)/(x^2 -1] + 2/(x^2 -1)
==> [x^2 -x -x^2 -x +2](x^2 -1)
==> [2-2x]/(x+1)(x-1)
==> -2(x-1)/(x+1)(x-1)
==> -2/(x+1)
Answer is C. −2/(x+1)
Above can be written as
==> [x(x-1)/(x^2 -1] - [x(x+1)/(x^2 -1] + 2/(x^2 -1)
==> [x^2 -x -x^2 -x +2](x^2 -1)
==> [2-2x]/(x+1)(x-1)
==> -2(x-1)/(x+1)(x-1)
==> -2/(x+1)
Answer is C. −2/(x+1)
25 Apr 2017, 09:11
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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. \(\frac{−2}{(x − 1)}\)
A. \(\frac{(−x + 3)}{(x + 1)}\)
B. \(\frac{2}{(x + 1)}\)
C. \(\frac{−2}{(x + 1)}\)
D. \(\frac{2}{(x − 1)}\)
E. \(\frac{−2}{(x − 1)}\)
Let’s get each fraction in terms of the common denominator of (x + 1)(x - 1).
[x(x - 1)]/[(x - 1)(x + 1)] - [x(x + 1)]/[(x - 1)(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
