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Given this equation (containing one variable $x$, and one parameter $a$):

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

I need to solve this equation and "discuss its solutions" depending on the parameter $a$. The proposed correct answer is:

  • If $a = 0, a = 1, a = -1$, then the equation doesn't have a solution
  • Otherwise, the solution is $x = \dfrac{a^2 + 1}2$

I don't know how to get to this answer. Could you enlighten me, please?

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    Have you tried seeing what happens if you make the suggested replacements of $a$?2011-12-07
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    @J.M. For `a = 1` and `a = -1` the equation is indeed unsolvable. For `a = 0` the solution is undefined ( `x = x` ). The problem is that I don't know how to get to this answer.2011-12-07
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    The first bulleted statement isn’t quite correct: if $a=0$, every real number except $0$ is a solution.2011-12-07
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    @Brian Yes, I agree. I got the proposed answer from a friend over the telephone, so it could be incomplete / partially wrong. If $a = 0$, then $x = x$ (the solution is "not defined", at least that's how we refer to this case here in Croatia).2011-12-07

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