Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

According to the solution to a problem, the following equation holds true:

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

I can't see a way for this to work out.

share|cite|improve this question
The equation does not hold at $x = -1$. – Makoto Kato Jan 2 '13 at 2:47
up vote 7 down vote accepted

I realised the answer while writing the question.

$(x-1)+2$ equals $x+1$ and cancels out the same fraction in the denominator.

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

Edit: As pointed out in the commentary, this doesn't hold true if $x= \pm 1$, as that would divide by zero.

share|cite|improve this answer
The equality does not make sense when $x = -1$. – Makoto Kato Jan 2 '13 at 1:44
Congratulations on the correct answer, but do mention that $x≠±1$ since the fraction would become undefined in the opposite case. – Parth Kohli Jan 3 '13 at 13:58

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.