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Question

# Write out the form of the partial fraction decomposition of :$\frac{3 x-1}{(x-3)(x+4)}$(Do not find the numerical values of the coefficients.)

Solution

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The factors $x-3$ and $x+4$ are both linear and appear to the first power, so each contributes one term to the partial fraction decomposition by the linear factor rule. Therefore, the decomposition has the form:

\begin{aligned} \dfrac{3x-1}{(x-3)(x+4)}&=\dfrac{A}{x-3}+\dfrac{B}{x+4}\\ \end{aligned}

where $A$ and $B$ are constants to be determined.

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