Explanation

(1 + 1/x)(1 + 1/(x+1))(1 + 1/(x+2))(1 + 1/(x+3))

= ((x+1)/x)((x+2)/(x+1))((x+3)/(x+2))((x+4)/(x+3))

Notice that the denominators and numerators cancel out:

= (x+4)/x