Structural Operations on Rational Expressions
|ExpandNumerator[expr]||expand numerators only|
|ExpandDenominator[expr]||expand denominators only|
|Expand[expr]||expand numerators, dividing the denominator into each term|
|ExpandAll[expr]||expand numerators and denominators completely|
ExpandNumerator writes the numerator of each term in expanded form.
Expand expands the numerator of each term, and divides all the terms by the appropriate denominators.
ExpandDenominator expands out the denominator of each term.
ExpandAll does all possible expansions in the numerator and denominator of each term.
|ExpandAll[expr,patt], etc.||avoid expanding parts which contain no terms matching patt|
|Together[expr]||combine all terms over a common denominator|
|Apart[expr]||write an expression as a sum of terms with simple denominators|
|Cancel[expr]||cancel common factors between numerators and denominators|
|Factor[expr]||perform a complete factoring|
Together puts all terms over a common denominator.
You can use Factor to factor the numerator and denominator of the resulting expression.
Apart writes the expression as a sum of terms, with each term having as simple a denominator as possible.
Cancel cancels any common factors between numerators and denominators.
Factor first puts all terms over a common denominator, then factors the result.
In mathematical terms, Apart decomposes a rational expression into "partial fractions".
In expressions with several variables, you can use Apart[expr,var] to do partial fraction decompositions with respect to different variables.