SOLUTION: Please help - need to solve: x/x^2-1 = 1/x+1 + 1/x^2-1

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Question 59041: Please help - need to solve:
x/x^2-1 = 1/x+1 + 1/x^2-1
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%5E2-1%29=1%2F%28x%2B1%29%2B1%2F%28x%5E2-1%29 First factor your denominators.
x%2F%28%28x%2B1%29%28x-1%29%29=1%2F%28x%2B1%29%2B1%2F%28%28x%2B1%29%28x-1%29%29
Your LCD is (x+1)(x-1) and x cannot = -1 or +1 or your denominator will equal 0. If you get -1 or +1 for your answer it is extraneous and can't be used.
Multiply every thing by (x+1)(x-1) and your denominators will all be eliminated.


x=x-1%2B1
x=x
x-x=x-x
0=0
The solution is all real numbers because this is an identity. No matter what you put in for x (within the domain) you will get both sides of the equation are equal. Pick some random numbers besides 1 and -1 and see for yourself.
:
There's easier ways to do this, but you would have to notice some things like if you subtract 1/(x^2-1) from both sides you get:
(x-1)/(x^2-1)=1/(x+1)
(x-1)/((x+1)(x-1))=1/(x+1) cancel and you have:
1/(x+1)=1/(x+1) They're identical.
Happy Calculating!!!