 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1/2/b/solution

Since

x^{2} - 1 = (x - 1) (x + 1)

A / (x - 1) + B / (x + 1)

. Matching the numerator gives

A + B = 1

and

A - B = 2

, hence

\frac{x + 2}{x ^{2} - 1} = \frac{3}{2 ( x - 1 )} - \frac{1}{2 ( x + 1 )}, x \neq = \pm 1.

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