How will (x^2 + 1) / (x^2 - 1) reduce to -1/(x + 1) + 1/(x-1) +1?

Question

anonymous · Answer

$$(x^2 + 1) \div (x^2 - 1) $$$$-1/(x + 1) + 1/(x-1) +1$$

espex · Answer

The process you need is to factor the top and bottom, split with a common denominator and reduce.

anonymous · Answer

Will you please do that for me? :)

espex · Answer

Try taking them one at a time, the numerator is$$x^2+1$$ which is the same as writing $$x^2+1^2$$ So how would you factor that?

anonymous · Answer

I am clueless.

espex · Answer

Start by noticing that with the second term as a positive any FOIL you do should produce a middle term. So you want to see how you can morph it without changing the value. So what if you factored out a -1? $$-1(-x^2-1)$$ How could you factor this? Try writing the terms next to it that would be required to produce the part you're looking for.