Question: Division by zero

assume(x>0);
assume(lambda>=0);

f:=(x,lambda)->2/(1+lambda)*1/( 1/(x+lambda)+1/(1+lambda));

                                 2                   
(x, lambda) -> --------------------------------------
                            /    1            1     \
               (1 + lambda) |---------- + ----------|
                            \x + lambda   1 + lambda/

ftilde:=(x,lambda)->1/2*(x+1-(x-1)^2*f(0,lambda)/f(x,lambda));

                                2             
               1     1   (x - 1)  f(0, lambda)
(x, lambda) -> - x + - - ---------------------
               2     2      2 f(x, lambda)    

ftilde(0,lambda);

                                      0

simpleftilde:=(x,lambda)->simplify(ftilde(x,lambda));

(x, lambda) -> simplify(ftilde(x, lambda))
simpleftilde(x,lambda);

     /                                     2                 2           2\
   x \-x - 4 lambda - 3 lambda x - 6 lambda  - 1 + 2 x lambda  + lambda x /
 - ------------------------------------------------------------------------
                        2 (1 + 2 lambda) (x + lambda)                      
simpleftilde(x,0);

Error, (in f) numeric exception: division by zero
f(x,0);

                                      2  
                                    -----
                                    1    
                                    - + 1
                                    x