We describe differential rational normal forms of a rational
function and their properties. Based on these normal forms,
we present an algorithm which, given a hyperexponential
function T(x), constructs two hyperexponential functions T1(x)
and T2(x) such that T(x) = T1'(x) + T2(x) and T2(x) is minimal
in some sense. The algorithm can be used to accelerate the
differential Gosper's algorithm and to compute right factors
of the telescopers.