algebra/ question

Question

Express -2x/[(x+1)(x²+1)] as a sum of partial fractions and hence write [x⁴+x³+x²-x]/(x+1)(x²+1) as a sum of partial fractions.

Answer 1

-2x/[x+1)(x²+1) = A/(x+1) + (Bx+C)/(x²+1), identically

-2x = Ax² + A +Bx² + Cx Bx + C

A+B = 0

B+C = -2

A+C = 0

A = 1, B = C = -1

 

Hence, (x⁴ + x³ + x² - x)/[(x+1)(x²+1) = 1 + [1/(x+1)] - [(x+1)/(x²+1)]