Question 59041
{{{x/(x^2-1)=1/(x+1)+1/(x^2-1)}}}  First factor your denominators.
{{{x/((x+1)(x-1))=1/(x+1)+1/((x+1)(x-1))}}}  
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)(x-1)/((x+1)(x-1))=1(x+1)(x-1)/(x+1)+1(x+1)(x-1)/((x+1)(x-1))}}}
{{{x*cross((x+1)(x-1))/cross((x+1)(x-1))=1*cross((x+1))*(x-1)/cross((x+1))+1*cross((x+1)(x-1))/cross((x+1)(x-1))}}}
{{{x=x-1+1}}}
{{{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!!!