Partial Fractions

To expand a quotient of polynomials into partial fractions, select the expression and either:

If the expression contains more than one variable, you must also type a comma, followed by the variable you want to perform the partial fractions decomposition with respect to, after "parfrac." Then press [Enter].

Examples:

Partial fraction decomposition

If the expression contains more than one variable, type a comma, followed by the variable for the partial fractions decomposition.

Partial fractions decomposition of an expression with two variables

Expressions With Irrational Roots

By default, Mathcad performs a partial fractions decomposition over the field of rational numbers. That is, if the initial expression is a quotient of polynomials with rational coefficients, the polynomials in the result also have rational coefficients. For example,

Partial fractions decomposition over the rationals

To perform a further decomposition of one of the terms in the expression, apply "parfrac" to just that term and type the root of the denominator as an argument after "parfrac." For example, you can apply "parfrac" to the first term in the preceding result, whose denominator has Square root of 2 as a root, as follows:

Partial fractions decomposition for denominator x squared minus 2

Note: Do not use the argument Square root of 2 with the original expression - just with the term whose denominator has Square root of 2 as a root.

Notes:

QuickSheet - Symbolic Calculus

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