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If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ?

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If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ? [#permalink]

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New post 20 Apr 2017, 23:19
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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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Re: If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ? [#permalink]

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New post 21 Apr 2017, 01:53
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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)
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Re: If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ? [#permalink]

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New post 25 Apr 2017, 09:11
Bunuel wrote:
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. \(\frac{−2}{(x − 1)}\)


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
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If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ? [#permalink]

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New post 25 Apr 2017, 09:30
Bunuel wrote:
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. \(\frac{−2}{(x − 1)}\)



Hi..

Another method apart from the one choosen above.
May be good for those find algebra difficult..
substitute x as 2 & find value in equation and match with choices

\(\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}= \frac{2}{(2 + 1)} − \frac{2}{(2 − 1)} + \frac{2}{(2^2 − 1)}= \frac{2}{3} − 2 + \frac{2}{3}=\frac{-2}{3}\)

Let's check the choices..

A. \(\frac{(−x + 3)}{(x + 1)}=\frac{1}{3}\)... NO

B. \(\frac{2}{(x + 1)}=\frac{2}{3}\).. NO

C. \(\frac{−2}{(x + 1)}=\frac{-2}{3}\)... YES

D. \(\frac{2}{(x − 1)}=2\)... NO

E. \(\frac{−2}{(x − 1)}=-2\).. NO

C
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Re: If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ? [#permalink]

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New post 27 Apr 2017, 11:31
1
\(\frac{{x(x+1) - x(x-1) +2 }}{{(x^2 - 1)}}\)

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

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

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

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

Ans: Option C
Re: If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ?   [#permalink] 27 Apr 2017, 11:31
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If x^2 ≠ 1, which is equal to x/(x + 1) − x/(x − 1) + 2/(x^2 − 1) ?

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