Originally Posted by
looseenz2 Could you please explain what you did between the last two steps? I'm not entirely sure what you did.
the basic rule is ...
when the numerator has a degree $\displaystyle \ge$ the degree of the denominator, divide the fraction.
this can be done with long division (as shown below), or the "shortcut" shown by mr. F
Code:
........1
----------
x^2+1 | x^2
........x^2 + 1
..... -----------
........... - 1
the quotient is $\displaystyle 1 + \frac{-1}{x^2+1} = 1 - \frac{1}{x^2+1}
$