A single fraction with linear factors in the denominator can be split into two or more fractions, known as partial fractions

There are three types:

• \(\dfrac{px+q}{(x+a)(x+b)}=\dfrac{A}{x+a}+\dfrac{B}{x+b}\)


• \(\dfrac{px^2+qx+r}{(x+a)(x+b)(x+c)}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{x+c}\)


• \(\dfrac{px^2+qx+r}{(x+a)(x+b)^2}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{(x+b)^2}\)

The constants \(A\), \(B\) and \(C\) can be found by either substitution or equating coefficients.

Partial fractions are used for integration and binomial expansions.