I really do not know how to do this problem and it is really upsetting me :(

Please put parentheses around the exponent. Right now it looks like you have

(x^(-4) x + 8)/(5 x - 3)

= (x^(-3) + 8)/(5 x - 3)

= ((1/x)^3 + 2^3)/(5 x - 3)

=(1/x + 2)((1/x)^2 + 2/x + 4)/(5 x - 3)