Why Maple not simplify
simplify((x*ln(x)-ln(1/(1+x))-x*ln(x/(1+x)))/((1+x)*ln(1+x)))
(result = 1) ?

I found following bug:

p := proc (k) sum((-1)^n*n/(factorial(k-n)*factorial(n)), n = 1 .. k) end proc; 

sum(p(k), k = 1 .. 1); 

sum(p(1), k = 1 .. 1); 

p(1)

Results must be same, but output is 0 (bug!), -1 (correct), -1 (correct)