Mathematical Methods in the Physical Sciences · Problem 2.13

LINEAR EQUATIONS; VECTORS, MATRICES, AND DETERMINANTS — Mary Boas

Mathematics — Methods · row-reduction-partial-fractions

Problem

In order to expand in partial fractions

\frac{px^2 + qx + r}{(x-a)(x-b)^2} = \frac{A}{x-a} + \frac{B}{x-b} + \frac{C}{(x-b)^2},

we need to solve the following equations for

A

B

C

\begin{cases} A + B = p \\ 2bA + (a+b)B - C = -q \\ b^2 A + abB - aC = r \end{cases}

Use row reduction to find

A

B

C

in terms of

a

b

p

q

, and

r