YES , we can put directly ..there is no need to be in product form etc...BUT if you have doubt then you can use an alternative approach :
simply take LCM first in denominator then you will get
lim x / ( x + sinx )
x->0
now since its 0/0 form so we can apply hopital's method hence just differenciate in numerator and denominator independently with respect to x , so we will get ,
lim 1 / (1 + cosx )
x->0
now put the limit i.e x=0 in the above expression :
ans = 1/2 ( since cos0 =1 )