If we take a fraction \(\dfrac{a}{b}\), and write it as the sum of two or more fractions whose denominators are factors of \(b\), then we have expressed it as a set of *partial fractions*.

For example, if we write \[\frac{1}{6} = \frac{1}{2} - \frac{1}{3}\] then \(1/2\) and \(-1/3\) are called partial fractions.

Similarly, we can write \[\frac{3}{(x-1)(x+2)}=\frac{1}{x-1}-\frac{1}{x+2} .\]