Factoring Problem

JHB

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Jan 31, 2011
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The question is: Find the constants A and B so that

((x^2)-1)/((x^2)-1)= 1+ [A/(x+1)]+[B/(x-1)]

Now, I know that I can change 1 into the multiplicative identity of x squared minus 1 over itself. I also know that to combine the other two terms, I will have to multiply them by (x-1) and (x+1) respectively. Each time I try a different combination, the result comes out too large. Any ideas?
 
JHB said:
((x^2)-1)/((x^2)-1)= 1+ [A/(x+1)]+[B/(x-1)]
Left side simplifies to 1; so:
A / (x+1) = -B / (x-1)
x = (A - B) / (A + B)

You sure you got that equation typed out properly; no typos?
 
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