Chapter 11, Problem 61RE

To determine

To calculate: the partial function decomposition of each rational expression.

Answer to Problem 61RE

Solution: $\frac{3}{x}+\frac{4}{x^2}-\frac{3}{x-1}$

Explanation of Solution

  $\frac{x-4}{x^2(x-1)}$

  $\begin{array}{l}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1}\\ \Rightarrow Ax(x-1)+B(x-1)+C{x}^2=x-4\end{array}$

Put $x=0\Rightarrow B=4$

Put $x=1\Rightarrow C=-3$

Since, coefficient of $x^2=0$

  $\begin{array}{l}A+C=0\\ A=3\end{array}$

  $\frac{3}{x}+\frac{4}{x^2}-\frac{3}{x-1}$