Answer:
[tex]x^3-x^2+x-1+\frac{2}{x+1}[/tex]
Step-by-step explanation:
See the picture attached.
Notice how I set up [tex]x^4+1[/tex] as [tex]x^4+0x^3+0x^2+0x+1[/tex], as it makes it easier to solve.
Also, notice that the 2 as the remainder doesn't have anything else to divide to, so that means there will be an extra term [tex]\frac{2}{x+1}[/tex] in the end of the answer.
