Question

If \[ \frac{x}{(x-1)^2(x+2)} = \frac{A}{(x-1)^2} + \frac{2}{9(x-1)} + \frac{B}{x+2}, \] then \(A+B=\)

• A. \(\frac{1}{3}\)
• B. \(\frac{1}{9}\)
• C. \(-\frac{1}{3}\)
• D. \(\frac{2}{3}\)

Hint:

In partial fractions, substitute the roots of denominator factors to quickly find unknown constants.

Answer 1

The Correct Option is B