a)`(3x^2+5x+1)/(x^3-1)-(1-x)/(x^2+x+1)-3/(x-1)`
`=(3x^2+5x+1)/((x-1)(x^2+x+1))-(1-x)/(x^2+x+1)-3/(x-1)`
`=(3x^2+5x+1-(1-x)(x-1)-3(x^2+x+1))/((x-1)(x^2+x+1))`
`=(3x^2+5x+1+x^2-2x+1-3x^2-3x-3)/((x-1)(x^2+x+1))`
`=(x^2-1)/((x-1)(x^2+x+1))`
`=((x-1)(x+1))/((x-1)(x^2+x+1))`
`=(x+1)/(x^2+x+1)`
b)`1/(x^2-x+1)+1-(x^2+2)/(x^3+1)`
`=1/(x^2-x+1)+1-(x^2+2)/((x+1)(x^2-x+1))`
`=(x+1+x^3+1-x^2-2)/((x+1)(x^2-x+1))`
`=(x^3-x^2+x)/((x+1)(x^2-x+1))`
`=(x(x^2-x+1))/((x+1)(x^2-x+1))`
`=x/(x+1)`
c)`7/x-x/(x+6)+36/(x^2+6x)`
`=7/x-x/(x+6)+36/(x(x+6))`
`=(7.(x+6)-x^2+36)/(x(x+6))`
`=(7x+42-x^2+36)/(x(x+6))`
`=(-x^2+7x+78)/(x(x+6))`
`=((13-x)(x+6))/(x(x+6))`
`=(13-x)/x`