Answer: [tex]\bold{\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}}[/tex]
Step-by-step explanation:
Factor both denominators to see which factors are missing from each denominator. Then multiply both fractions so they have the same LCD.
[tex]\dfrac{s^3}{s^2-2s+1}+\dfrac{-2}{s^2-4s+3}[/tex]
[tex]=\dfrac{s^3}{(s-1)(s-1)}+\dfrac{-2}{(s-1(s-3)}[/tex]
[tex]=\dfrac{s^3}{(s-1)(s-1)}\bigg(\dfrac{s-3}{s-3}\bigg)+\dfrac{-2}{(s-1(s-3)}\bigg(\dfrac{s-1}{s-1}\bigg)[/tex]
[tex]=\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}[/tex]
