how to simplify (2x+1)/(x-1)*(x+2)

to get {1/(x-1)}+{(1/(x+2)}

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- Jul 10th 2013, 10:18 AMabdulrehmanshahsimplifying equation
how to simplify (2x+1)/(x-1)*(x+2)

to get {1/(x-1)}+{(1/(x+2)} - Jul 10th 2013, 10:55 AMadkinsjrRe: simplifying equation
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 $\displaystyle \frac{A}{x-1}+\frac{B}{x+2}$