# The Partfrac Function; The Fcoef Function - HP 49g+ User Manual

Graphing calculator.

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:
PARTFRAC('(2*X^6-14*X^5+29*X^4-37*X^3+41*X^2-16*X+5)/(X^5-
7*X^4+11*X^3-7*X^2+10*X)') =
'2*X+(1/2/(X-2)+5/(X-5)+1/2/X+X/(X^2+1))'
This technique is useful in calculating integrals (see chapter on calculus) of
rational fractions.
If you have the Complex mode active, the result will be:
'2*X+(1/2/(X+i)+1/2/(X-2)+5/(X-5)+1/2/X+1/2/(X-i))'

### 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)/(X--3)^5*(X-1)^2'
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