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

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on Nov 16, 2024 at 8:36 pm



You asked:

Evaluate the expression: 3x2+2x+1x3−1−1−xx2+x+1−2x−1\frac{3 {x}^{2} + 2 x + 1}{{x}^{3} - 1} - \frac{1 - x}{{x}^{2} + x + 1} - \frac{2}{x - 1}

MathBot Answer:

Evaluated



3x2+2x+1x3−1−1−xx2+x+1−2x−1=−1−xx2+x+1−2x−1+3x2+2x+1x3−1\displaystyle \frac{3 {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

3x2+2x+1x3−1−1−xx2+x+1−2x−1=3x2x3−1+xx2+x+1+2xx3−1−1x2+x+1−2x−1+1x3−1\frac{3 {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

3x2+2x+1x3−1−1−xx2+x+1−2x−1=2xx2+x+1\frac{3 {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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