Rút gọn biểu thức

To simplify the expression, we need to perform the operations in the following order:

1. Simplify each fraction individually.
2. Combine the fractions using the appropriate operations.

Let's start by simplifying each fraction:

1. (4a^2 - 3a + 5) / (a^3 - 1)
Factor the numerator: 4a^2 - 3a + 5 = (4a - 1)(a + 5)
Factor the denominator: a^3 - 1 = (a - 1)(a^2 + a + 1)
Simplified fraction: (4a - 1)(a + 5) / (a - 1)(a^2 + a + 1)

2. -1 - 2a
This fraction is already simplified.

3. (a^2 + a + 1) - 6
Simplify the numerator: a^2 + a + 1 - 6 = a^2 + a - 5

4. 4 - 1
Simplify the fraction: 4 - 1 = 3

Now, we can combine the fractions using the appropriate operations:

[(4a - 1)(a + 5) / (a - 1)(a^2 + a + 1)] - (-1 - 2a) + (a^2 + a - 5) / 3

This is the simplified expression.