Question

If \( \frac{x+1}{x^3(x-1)} = \frac{a}{x} + \frac{b}{x^2} + \frac{c}{x^3} + \frac{d}{x-1} \) then

• A. a = b = c = -d
• B. a = b = 2c = -d
• C. a = 2b = c = -d
• D. a = b = 2c = d

Hint:

When dealing with repeated linear factors in partial fractions like \(x^3\), the "cover-up" method only works for the highest power (finding 'c' by setting x=0). For the other coefficients (a and b), comparing coefficients or substituting other convenient values (like x=-1) is necessary.

Answer 1

The Correct Option is B