Once we have found the constants A, B,C,G,H,M we can substitute them into decompk and obtain the partial fraction decomposition of k. Since , we obtain the partial fraction decomposition of m by subsituting the constants into decompk and adding the polynomial. Let's call the result of this operation decm. As long as all coefficients in your expression are rationals in a non-decimal form, both commands are, in fact, telling Maple to find a factorization or a partial fraction decomposition using only rational numbers as constants. If your polynomial or the denominator of your rational function happen to have irrational roots, the commands may not work at all.
Maple can deal with irrational roots in several ways.
The best approach is to tell Maple to look for a factorization or a partial fraction decomposition which allows arbitrary real numbers, not just rationals. Maple will respond by returning a partial fraction decomposition or a factorization in which coefficients and roots are floating point approximations of their exact values. For all practical purposes floating point approximations of exact values are usually sufficient. Incidentally, if coefficients of a polynomial or a rational function contain a decimal expression, Maple will automatically factor or decompose using real numbers. Engineers often prefer partial fraction decompositions using complex numbers.