PartialFractionSteps - Maple Help
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Student[Basics]

 PartialFractionSteps
 generate steps in factoring polynomials

 Calling Sequence PartialFractionSteps( expr, variable )

Parameters

 expr - string or expression variable - (optional) variable to collect the terms by implicitmultiply - (optional) truefalse output = ... - (optional) option to control the return value displaystyle = ... - (optional) option to control the layout of the steps

Description

 • The PartialFractionSteps command accepts a polynomial and displays the steps required to perform a partial fraction decomposition.
 • If no variable is given, then a variable is chosen by calling indets.  When the expression is multivariate, the first indeterminate is used.
 • If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.
 • The implicitmultiply option is only relevant when expr is a string.  This option is passed directly on to the InertForm:-Parse command and will cause things like 2x to be interpreted as 2*x, but also, xyz to be interpreted as x*y*z.
 • The output and displaystyle options are described in Student:-Basics:-OutputStepsRecord. The return value is controlled by the output option.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{PartialFractionSteps}\left(-\frac{4x}{\left(x+3\right)\left(x+2\right)}\right)$
 $\begin{array}{lll}{}& {}& {-}\frac{{4}{}{x}}{\left({x}{+}{3}\right){}\left({x}{+}{2}\right)}\\ \text{•}& {}& \text{First, factor the numerator and denominator. If we can simplify by dividing terms, we do so.}\\ {}& {}& {-}\frac{{4}{}{x}}{\left({x}{+}{3}\right){}\left({x}{+}{2}\right)}\\ \text{•}& {}& \text{Use the factors to write an equation for the partial fraction decomposition}\\ {}& {}& {-}\frac{{4}{}{x}}{\left({x}{+}{3}\right){}\left({x}{+}{2}\right)}{=}\frac{{A}}{{x}{+}{2}}{+}\frac{{B}}{{x}{+}{3}}\\ \text{•}& {}& \text{Multiply by the LHS's denominator.}\\ {}& {}& {-}{4}{}{x}{=}\left(\frac{{A}}{{x}{+}{2}}{+}\frac{{B}}{{x}{+}{3}}\right){}\left({x}{+}{3}\right){}\left({x}{+}{2}\right)\\ \text{•}& {}& \text{Expand everything out.}\\ {}& {}& {-}{4}{}{x}{=}{A}{}{x}{+}{B}{}{x}{+}{3}{}{A}{+}{2}{}{B}\\ \text{•}& {}& \text{Equate the coefficients to create equations}\\ {}& {}& \left[{0}{=}{3}{}{A}{+}{2}{}{B}{,}{-4}{=}{A}{+}{B}\right]\\ \text{•}& {}& \text{Solve the equations.}\\ {}& {}& \left[{A}{=}{8}{,}{B}{=}{-12}\right]\\ \text{•}& {}& \text{Use these values in the partial fraction decomposition and simplify. The final partial fraction decomposition is}\\ {}& {}& \frac{{8}}{{x}{+}{2}}{-}\frac{{12}}{{x}{+}{3}}\end{array}$ (1)

Compatibility

 • The Student[Basics][PartialFractionSteps] command was introduced in Maple 2024.
 • For more information on Maple 2024 changes, see Updates in Maple 2024.