Why is it that (s+1)/(s^2-1) can be written 1/(s-1)?

 

s^2 -1 can be factorised to (s + 1)(s - 1).

then divide both sides by s + 1

 

s^2 -1 can be factorised to (s + 1)(s - 1).

then divide both sides by s + 1

more generally, s^2 -1 is a difference of squares, (s^2 - 1^2). the general difference of squares (x^2 - a^2) factors to (x+a)(x-a)