Question

If \[ \frac{x+3}{(1-x)^2(1+x^2)} = \frac{A}{(1-x)} + \frac{B}{(1-x)^2} + \frac{Cx+D}{2(1+x^2)}, \] then \(B^2+C^2+D^2=\)

• A. \(\dfrac{3}{4}\)
• B. \(\dfrac{9}{2}\)
• C. \(14\)
• D. \(4\)

Hint:

For repeated linear factors in partial fractions, \[ \boxed{\text{Substitute the repeated root first to obtain the highest power coefficient.}} \] The remaining constants can then be found using differentiation or coefficient comparison.

Answer 1

The Correct Option is C