Problem understanding proof of combinations

on the left term its basically going from 1/(r-1)! to r/r!.. cancel the r from the second (if we divide top and bottom by r, the top goes to 1, and we subtract 1 from the factorial) and it goes back to 1/(r-1)!

a little harder to see with the right term but its the same too

so from 1/(n-r)! to (n-r+1)/(n-r+1)!

we can again see the second term cancels, so we eliminate the top of the fraction back to 1, and subtract 1 from the denominator, leaving it as 1/(n-r)!

hopefully ive explained it well and explained the right bit u were asking about :P