$$\frac{x-2x^2 +3}{x^3-1}$$
You asked:
Evaluate the expression: \(\frac{x - 2 {x}^{2} + 3}{{x}^{3} - 1}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{x - 2 {x}^{2} + 3}{{x}^{3} - 1} = \frac{- 2 x^{2} + x + 3}{x^{3} - 1} \)
Expanded
\[\frac{x - 2 {x}^{2} + 3}{{x}^{3} - 1} = - \frac{2 x^{2}}{x^{3} - 1} + \frac{x}{x^{3} - 1} + \frac{3}{x^{3} - 1}\]
Factored
\[\frac{x - 2 {x}^{2} + 3}{{x}^{3} - 1} = - \frac{\left(2 x - 3\right) \left(x + 1\right)}{\left(x - 1\right) \left(x^{2} + x + 1\right)}\]