Partial Fraction Decomposition

Question

Determine the coefficients D, E, and F in the p.f.d.

[2x^4 +x^3 -2x +4] / (x+1)^7 = A/(x+1)^7 +B/(x+1)^6 +C/(x+1)^5 +D/(x+1)^4 +E/(x+1)^3 +F/(x+1)^2 +G/(x+1) +H

Answer 1

2x^4 +x^3 -2x +4 = A + B(x + 1) + C(x +1)² + D(x + 1)³ + E(x + 1)⁴ + F(x + 1)⁵ + G(x + 1)⁶ + G(x + 1)⁷

Expand, collect like terms, arrange in descending degree, and solve for D, E, and F.