Partial fractions My approach But I just get garbage out so

Partial fractions:

My approach:

But I just get garbage out, so what am I doing wrong?

Solution

The denominator will remain common to all the fractions. The denominator is s³ ( s² -s) = s⁴(s -1). Therefore, the given fraction is [(2s⁴ - 2s³) / s⁴(s -1)] + [ (s² + 1)/s⁴(s - 1)] = [ 2s³( s - 1)/  s⁴(s -1)] + [ (s² + 1)/s⁴(s - 1)] = 2/s + [ (s² + 1)/s⁴(s - 1)]