What is expand 1/(1+0.5x^{-1)} ?

The solution to expand 1/(1+0.5x^{-1)} is x/(x+0.5)

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expand 1/(1+0.5x^{-1)}

expand

\frac{1}{1 + 0.5 x ^{- 1}}

\frac{x}{x + 0.5}

Solution steps

\frac{1}{1 + 0.5 x ^{- 1}}

0.5 x^{- 1} = \frac{0.5}{x}

= \frac{1}{1 + \frac{0.5}{x}}

Join

1 + \frac{0.5}{x} : \frac{x + 0.5}{x}

= \frac{1}{\frac{x + 0.5}{x}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x}{x + 0.5}

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What is expand 1/(1+0.5x^{-1)} ?
The solution to expand 1/(1+0.5x^{-1)} is x/(x+0.5)