What are the steps to rewriting x^2/x-1 as (x + 1) + (1/x-1)?

Question

anonymous · Answer

It's hard to read like that, here it is formatted:
$$x^2/(x-1) = x+1+x^2/(x-1)$$

anonymous · Answer

I believe you wrote the formatted equation incorrectly. It confused me for a second! Shouldn't it be:
$$x^2/x-1 = (x+1)+1/x-1$$

Anyways...My calculus professor constantly reminds our class of two of the greatest mathematic 'tricks' : adding 0 and multiplying by 1. These two tricks are ways to backtrack through equations which have been simplified and, as a result, are missing parts to the equation.

This problem requires you to add 0.

Instead of simply $$x^2 / x-1$$, write it as $$x^2 -1+1/x-1$$

From there, you can split the fraction into two parts, and simplify both. Good luck!

anonymous · Answer

Oops, yes that should have been a 1 instead of a x^2 in the rewrite.  Thank you so much, I see it now! :)

anonymous · Answer

I'm glad to have helped you! Whenever you're searching for an answer and you can't see it, remember that you can also add 0 and multiply by 1 to find it!