Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.4 Partial Fractions, #18 · Calculus · Techniques of integration

What goes wrong if we look for … and … so that…

What goes wrong if we look for $A$ and $B$ so that
$\frac{x ^{2}}{( x - 3 ) ( x + 3 )} = \frac{A}{x - 3} + \frac{B}{x + 3} ?$
Over a common denominator, try to match the numerators. What to do first?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.4 Partial Fractions, #18

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