Answer
a) $x^{4}+4x^{2}+16+\frac{A}{(x-2)}+\frac{B}{(x+2)}$
b) $\frac{Ax+B}{x^{2}-x+1}+\frac{Bx+C}{x^{2}+2}+\frac{Ex+F}{(x^{2}+2)^2}$
Work Step by Step
a) $\frac{x^{6}}{x^{2}-4}$ = $x^{4}+4x^{2}+16+\frac{64}{(x-2)(x+2)}$ $=x^{4}+4x^{2}+16+\frac{A}{(x-2)}+\frac{B}{(x+2)}$
b) $\frac{x^{4}}{(x^{2}-x+1)(x^{2}+2)^2}$ = $\frac{Ax+B}{x^{2}-x+1}+\frac{Cx+D}{x^{2}+2}+\frac{Ex+F}{(x^{2}+2)^2}$