To add these fractions, we first need to find a common denominator.

The denominators are x^3 - 1, x^2 + x + 1, and x - 1. To find a common denominator, we need to factorize each denominator first.

x^3 - 1 factors as (x - 1)(x^2 + x + 1),
x^2 + x + 1 is already in its factored form,
x - 1 is already factored.

Therefore, the common denominator is (x - 1)(x^2 + x + 1).

Rewriting the fractions with the common denominator, we get:

(2x^2 + 7x + 9)/(x - 1)(x^2 + x + 1) + (3)/(x - 1)(x^2 + x + 1) - (5)/(x - 1)(x^2 + x + 1)

Now, we can add the numerators together:

(2x^2 + 7x + 9 + 3 - 5)/(x - 1)(x^2 + x + 1)
= (2x^2 + 7x + 7)/(x - 1)(x^2 + x + 1)

Therefore, the sum of the given fractions is (2x^2 + 7x + 7)/(x - 1)(x^2 + x + 1).