Answer
$$4x^2+2x+1$$
Work Step by Step
To simplify the equation, you first need to determine the factors of the numerator: $$8x^{3}-1 = (2x-1)(4x^2+2x+1)$$
The equation can now be rewritten as:
$$\frac{8x^{3}-1}{2x-1} = \frac{(2x-1)(4x^2+2x+1)}{2x-1}$$
Notice that the denominator $2x-1$ is similar with the first factor of $8x^{3}-1$; hence, we can cancel the term $(2x-1)$, and that gives us:
$$4x^2+2x+1$$
