How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?

1 answer:

Ber [7]4 years ago

3 0

$\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}$

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Step two:
Figure out what formula you need to use in order to solve in this case I'd use the Quadratic formula.

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$x = \frac{ - 9 + - \sqrt{73} }{2}$
Since you cannot solve this any further, your final two answers are...
$x = \frac{ - 9 + \sqrt{73} }{2}$
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