A single fraction with linear factors in the denominator can be split into two or more fractions, known as bpartial fractions/b
There are three types: ulli(\dfrac{px+q}{(x+a)(x+b)}=\dfrac{A}{x+a}+\dfrac{B}{x+b})/lili(\dfrac{px2+qx+r}{(x+a)(x+b)(x+c)}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{x+c})/lili(\dfrac{px2+qx+r}{(x+a)(x+b)2}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{(x+b)2})[/li]/ul The constants (A), (B) and (C) can be found by either bsubstitution/b or bequating coefficients/b.
Partial fractions are used for integration and binomial expansions.
There are three types of partial fractions:
[ul]li(\dfrac{px+q}{(x+a)(x+b)}=\dfrac{A}{x+a}+\dfrac{B}{x+b})/lili(\dfrac{px2+qx+r}{(x+a)(x+b)(x+c)}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{x+c})/lili(\dfrac{px2+qx+r}{(x+a)(x+b)2}=\dfrac{A}{x+a}+\dfrac{B}{x+b}+\dfrac{C}{(x+b)2})[/li]/ul