Partial Fractions

With the command Partial Fractions, you can write a rational expression as a sum of simpler fractions—essentially the reverse of the operation demonstrated in the previous section.

$\blacktriangleright$ To write a rational expression as a sum of rational expressions

1.
Enter the rational expression in mathematics mode.

2.
Leave the insertion point in the expression.

3.
From the Polynomials submenu (or from the Calculus submenu), choose Partial Fractions .

The Partial Fractions command expands a rational expression into a sum of rational expressions having denominators that are multiples of powers of linear and irreducible quadratic factors. In this case irreducible means the roots are neither rational nor rational combinations of the coefficients of the polynomials. This operation does not accept floating-point numbers, so write the coefficients as integers or quotients of integers. There is no automatic way to change a decimal to a fraction, such as .58 to ${\frac{{58}}{{100}}}$, but here again you can take advantage of the fact that you are working in a word processor. If more than one variable occurs in the expression, specify your choice of variable in the dialog box that appears.


\begin{example}
In each of the following cases, apply \textsf{Partial Fractions...
...-\frac{1}{\left(
x+1\right) \left( x-y\right) }
\end{eqnarray*}
\end{example}