How do I know that the expression: 1/(1−x)

How do I know that the expression:
$\frac{1}{1-x}$
Is equal to the infinite sum:
$-\left(\frac{1}{x}\right)-{\left(\frac{1}{x}\right)}^{2}-{\left(\frac{1}{x}\right)}^{3}-{\left(\frac{1}{x}\right)}^{4}+...$
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rcampas4i
$\begin{array}{rl}\frac{1}{1-x}=& \frac{1}{x\left[\frac{1}{x}-1\right]}\\ =& -\left(\frac{1}{x}\right)\frac{1}{1-\left(\frac{1}{x}\right)}\\ =& -\left(\frac{1}{x}\right)\left[1+{\left(\frac{1}{x}\right)}^{1}+{\left(\frac{1}{x}\right)}^{2}+{\left(\frac{1}{x}\right)}^{3}+{\left(\frac{1}{x}\right)}^{4}+\cdots \right]\end{array}$