Question

Write out the form of the partial fraction decomposition of the function (as in this example). do not determine the numerical values of the coefficients. (a) x4 − 2x3 + x2 + 7x − 5 x2 − 2x + 1 x2− a x−1​− b (x−1)2​ (b) x2 − 1 x3 + x2 + x

Answer 1

$\frac{x^{4}-2x^{3}+x^{2}+7x-5}{x^{2}-2x+1} = x^{2}+\frac{a}{x-1}+\frac{b}{(x-1)^{2}}$
It looks like your first selection (a) is appropriate.