(3x^2+2x+1)/(x^3-1)-(1-x)/(x^2+x+1)-2/(x-1)

asked by guest
on Nov 16, 2024 at 8:36 pm



You asked:

Evaluate the expression: \(\frac{3 \cdot {x}^{2} + 2 x + 1}{{x}^{3} - 1} - \frac{1 - x}{{x}^{2} + x + 1} - \frac{2}{x - 1}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{3 \cdot {x}^{2} + 2 x + 1}{{x}^{3} - 1} - \frac{1 - x}{{x}^{2} + x + 1} - \frac{2}{x - 1} = - \frac{1 - x}{x^{2} + x + 1} - \frac{2}{x - 1} + \frac{3 x^{2} + 2 x + 1}{x^{3} - 1} \)

Expanded

\[\frac{3 \cdot {x}^{2} + 2 x + 1}{{x}^{3} - 1} - \frac{1 - x}{{x}^{2} + x + 1} - \frac{2}{x - 1} = \frac{3 x^{2}}{x^{3} - 1} + \frac{x}{x^{2} + x + 1} + \frac{2 x}{x^{3} - 1} - \frac{1}{x^{2} + x + 1} - \frac{2}{x - 1} + \frac{1}{x^{3} - 1}\]

Factored

\[\frac{3 \cdot {x}^{2} + 2 x + 1}{{x}^{3} - 1} - \frac{1 - x}{{x}^{2} + x + 1} - \frac{2}{x - 1} = \frac{2 x}{x^{2} + x + 1}\]

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