 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/10/b/solution

A / (x - 4) + B / (x + 9)

13 (x + 1) = A (x + 9) + B (x - 4)

. Substitution at

x = 4

and

x = - 9

yields

A = 5

and

B = 8

, hence

\frac{13 ( x + 1 )}{( x - 4 ) ( x + 9 )} = \frac{5}{x - 4} + \frac{8}{x + 9}, x \neq = 4, - 9.

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