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

asked by guest
on Apr 06, 2025 at 9:01 pm



You asked:

Evaluate the expression: −x3(1−x)3+3x1−x−1\frac{-{x}^{3}}{{\left( 1 - x \right)}^{3}} + \frac{3 x}{1 - x} - 1

MathBot Answer:

Evaluated



−x3(1−x)3+3x1−x−1=−x3(1−x)3+3x1−x−1\displaystyle \frac{-{x}^{3}}{{\left( 1 - x \right)}^{3}} + \frac{3 x}{1 - x} - 1 = - \frac{x^{3}}{\left(1 - x\right)^{3}} + \frac{3 x}{1 - x} - 1

Expanded

−x3(1−x)3+3x1−x−1=−x3−x3+3x2−3x+1+3x1−x−1\frac{-{x}^{3}}{{\left( 1 - x \right)}^{3}} + \frac{3 x}{1 - x} - 1 = - \frac{x^{3}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{3 x}{1 - x} - 1

Factored

−x3(1−x)3+3x1−x−1=−3x3−9x2+6x−1(x−1)3\frac{-{x}^{3}}{{\left( 1 - x \right)}^{3}} + \frac{3 x}{1 - x} - 1 = - \frac{3 x^{3} - 9 x^{2} + 6 x - 1}{\left(x - 1\right)^{3}}

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