how to simplify (2x+1)/(x-1)*(x+2)
to get {1/(x-1)}+{(1/(x+2)}
You're trying to do a partial fraction decomposition.
$\displaystyle \frac{2x+1}{(x-1)(x+2)}=\frac{A}{x-1}+\frac{B}{x+2}$
$\displaystyle A(x+2)+B(x-1)=2x+1$
$\displaystyle x(A+B)+2A-B=2x+1$
Therefore $\displaystyle A+B=2$ and $\displaystyle 2A-B=1$. Solve for A and B and plug the solutions back into $\displaystyle \frac{A}{x-1}+\frac{B}{x+2}$