What is (1/(x^2)-1}{\frac{x-4)/5-1/x} ?

The solution to (1/(x^2)-1}{\frac{x-4)/5-1/x} is -(5(x-1))/(x(x-5))

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simplify (1/(x^2)-1}{\frac{x-4)/5-1/x}

simplify

\frac{\frac{1}{x ^{2}} - 1}{\frac{x - 4}{5} - \frac{1}{x}}

- \frac{5 ( x - 1 )}{x ( x - 5 )}

Solution steps

\frac{\frac{1}{x ^{2}} - 1}{\frac{x - 4}{5} - \frac{1}{x}}

Join

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

= \frac{\frac{- x ^{2} + 1}{x ^{2}}}{\frac{x - 4}{5} - \frac{1}{x}}

Join

\frac{x - 4}{5} - \frac{1}{x} : \frac{x ^{2} - 4 x - 5}{5 x}

= \frac{\frac{- x ^{2} + 1}{x ^{2}}}{\frac{x ^{2} - 4 x - 5}{5 x}}

Apply the fraction rule:

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

= \frac{( - x ^{2} + 1 ) \cdot 5 x}{x ^{2} ( x ^{2} - 4 x - 5 )}

Cancel

\frac{( - x ^{2} + 1 ) \cdot 5 x}{x ^{2} ( x ^{2} - 4 x - 5 )} : - \frac{( x - 1 ) \cdot 5}{x ( x - 5 )}

= - \frac{( x - 1 ) \cdot 5}{x ( x - 5 )}

= - \frac{5 ( x - 1 )}{x ( x - 5 )}

(p + 4)^{2}

4 (3 x + 5)

ln (0) + 1

3 x^{3} - 2 x + 1

\frac{x ^{2} + 4 x}{2 x + 8}

What is (1/(x^2)-1}{\frac{x-4)/5-1/x} ?
The solution to (1/(x^2)-1}{\frac{x-4)/5-1/x} is -(5(x-1))/(x(x-5))