I´m not sure how to explain it but I´ll give you my solution:
(c+1)/(c^2-1)-(c+1)/(1-c)=
= 1/(c-1) - (c+1)/(1-c) (conjugates)
= (1-c)/(c-1)(1-c) - (c+1)(c-1)/(c-1)(1-c) (common denominators)
= (1-c)+(-(c-1)(c+1))/ -(c-1)(c-1) the red text is replaced with 1 due to divison
= (1+ c+1)/(c-1)
=(c+2)/(c-1)
VSB
Good luck, if i have been unclear about something, ask me or someone else here:)