((x)/(2)-(1)/(x))^(5)

asked by guest
on Nov 15, 2024 at 8:33 am



You asked:

Evaluate the expression: \({\left( \frac{x}{2} - \frac{1}{x} \right)}^{5}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( \frac{x}{2} - \frac{1}{x} \right)}^{5} = \left(\frac{x}{2} - \frac{1}{x}\right)^{5} \)

Expanded

\[{\left( \frac{x}{2} - \frac{1}{x} \right)}^{5} = \frac{x^{5}}{32} - \frac{5 x^{3}}{16} + \frac{5 x}{4} - \frac{5}{2 x} + \frac{5}{2 x^{3}} - \frac{1}{x^{5}}\]

Factored

\[{\left( \frac{x}{2} - \frac{1}{x} \right)}^{5} = \frac{\left(x^{2} - 2\right)^{5}}{32 x^{5}}\]

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