What is (1-1/(x^2))/(1/x-1) ?

The solution to (1-1/(x^2))/(1/x-1) is -(x+1)/x

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

simplify

\frac{1 - \frac{1}{x ^{2}}}{\frac{1}{x} - 1}

- \frac{x + 1}{x}

Solution steps

\frac{1 - \frac{1}{x ^{2}}}{\frac{1}{x} - 1}

Join

1 - \frac{1}{x ^{2}} : \frac{x ^{2} - 1}{x ^{2}}

= \frac{\frac{x ^{2} - 1}{x ^{2}}}{\frac{1}{x} - 1}

Join

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

= \frac{\frac{x ^{2} - 1}{x ^{2}}}{\frac{- x + 1}{x}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( x ^{2} - 1 ) x}{x ^{2} ( - x + 1 )}

Cancel

\frac{( x ^{2} - 1 ) x}{x ^{2} ( - x + 1 )} : - \frac{x + 1}{x}

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

4 (x^{- 3} y^{4}) (- 3 x y^{2})^{2}

(3 y - 1)^{2}

\frac{33}{5 \times ( - \frac{81}{3} )}

(cos (x))^{2} - (sin (x))^{2}