 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/7/a/solution

A / (x - 3) + B / (x + 7)

. After multiplying through,

7 x + 29 = A (x + 7) + B (x - 3)

. Setting

x = 3

gives

A = 5

, and setting

x = - 7

gives

B = 2

, so

\frac{7 x + 29}{( x - 3 ) ( x + 7 )} = \frac{5}{x - 3} + \frac{2}{x + 7}, x \neq = 3, - 7.

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