Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.4 Partial Fractions, #17 · Calculus · Techniques of integration

Apply Method 1 (matching numerators) to Example 3: …\frac{1}{cy-by^2}=\frac{A}{y}+\frac{B}{c-by}=\frac{A(c-by)+By}{y(c-by)}.… Match the numerators…

Apply Method 1 (matching numerators) to Example 3:
$\frac{1}{cy - b y ^{2}} = \frac{A}{y} + \frac{B}{c - b y} = \frac{A ( c - b y ) + B y}{y ( c - b y )} .$
Match the numerators on the far left and far right. Why does $A c = 1$ ? Why does $- b A + B = 0$ ? What are $A$ and $B$ ?

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.4 Partial Fractions, #17

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