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

asked by guest
on Sep 20, 2024 at 1:40 pm



You asked:

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

MathBot Answer:

Evaluated



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

Expanded

\[\frac{1 - 2 x}{{\left( 1 + x \right)}^{2} \cdot {x}^{\frac{2}{3}}} = - \frac{2 x}{x^{\frac{8}{3}} + 2 x^{\frac{5}{3}} + x^{\frac{2}{3}}} + \frac{1}{x^{\frac{8}{3}} + 2 x^{\frac{5}{3}} + x^{\frac{2}{3}}}\]

Factored

\[\frac{1 - 2 x}{{\left( 1 + x \right)}^{2} \cdot {x}^{\frac{2}{3}}} = - \frac{2 x - 1}{x^{\frac{2}{3}} \left(x + 1\right)^{2}}\]

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