We have:

2/(x^2-1)(x^2+1)

by looking at this, what steps do I have to take to find out that it is equal to:

(1/(x^2-1)) - (1/(x^2+1))

?

You see I had to integrate this, and i did it by factoring completely the denominator then using partial fraction decomposition and i did get the right answer, however the book solution did not use PFD, and instead does that 'splitting of the fraction' as shown above, which then makes it rather easy to integrate then and there now that its been split since right away I can tell that it is an inverse tanh and an inverse tan, so it seems to involve less steps which saves time and effort.