The PROPFRAC function
The function PROPFRAC converts a rational fraction into a "proper" fraction,
i.e., an integer part added to a fractional part, if such decomposition is
possible. For example:
PROPFRAC('5/4') = '1+1/4'
PROPFRAC('(x^2+1)/x^2') = '1+1/x^2'
The PARTFRAC function
The function PARTFRAC decomposes a rational fraction into the partial
fractions that produce the original fraction. For example:
The FCOEF function
The function FCOEF is used to obtain a rational fraction, given the roots and
poles of the fraction.
Note: If a rational fraction is given as F(X) = N(X)/D(X), the roots of the
fraction result from solving the equation N(X) = 0, while the poles result from
solving the equation D(X) = 0.
The input for the function is a vector listing the roots followed by their
multiplicity (i.e., how many times a given root is repeated), and the poles
followed by their multiplicity represented as a negative number. For example,
if we want to create a fraction having roots 2 with multiplicity 1, 0 with
multiplicity 3, and -5 with multiplicity 2, and poles 1 with multiplicity 2 and –3
with multiplicity 5, use:
FCOEF([2 1 0 3 –5 2 1 -2 -3 -5]) = '(X—5)^2*X^3*(X-2)/9X—3)^5*(X-1)^2'
If you press µ you will get: