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Question

Write out the form of the partial fraction decomposition of :

3x1(x3)(x+4)\frac{3 x-1}{(x-3)(x+4)}

(Do not find the numerical values of the coefficients.)

Solution

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Answered 1 year ago
Answered 1 year ago
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The factors x3x-3 and x+4x+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:

3x1(x3)(x+4)=Ax3+Bx+4\begin{aligned} \dfrac{3x-1}{(x-3)(x+4)}&=\dfrac{A}{x-3}+\dfrac{B}{x+4}\\ \end{aligned}

where AA and BB are constants to be determined.

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