How do I do partial fractions??

How do I do partial fractions.

 

Hi Max :)

 

Here is an example.

 

\(\frac{4}{(x+2)(x-1)}=\frac{A}{x+2}+\frac{B}{x-1}\\ \frac{4}{(x+2)(x-1)}=\frac{Ax-A}{(x+2)(x-1)}+\frac{Bx+2B}{(x+2)(x-1)}\\ \frac{4}{(x+2)(x-1)}=\frac{Ax-A+Bx+2B}{(x+2)(x-1)}\\ Ax-A+Bx+2B=4\\ (A+B)x+2B-A=4\\ A+B=0 \qquad and \qquad 2B-A=4\\ A=-B \qquad and \qquad 2B-A=4\\ 2B--B=4\\ 3B=4\\ B=\frac{4}{3}\qquad and \qquad A=-\frac{4}{3}\\ so\\ \frac{4}{(x+2)(x-1)}=\frac{-4/3}{x+2}+\frac{4/3}{x-1}\\ \)

 

There are a number of you tube clips on this topic that will probably help more :)