What is ((1/(x+1)-1/(x-1)))/((1/(x-1)+1/(x+1))) ?

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

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simplify ((1/(x+1)-1/(x-1)))/((1/(x-1)+1/(x+1)))

simplify

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

- \frac{1}{x}

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

Apply the fraction rule:

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

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

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

Cancel

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

= - \frac{1}{x}

1.0 2^{12}

\frac{x ^{2} - 2 x - 15}{x ^{2} - 13 x + 40}

x^{2} - 5 x - 104

lo g_{10} (1 0^{1})

\frac{y ^{2} - 9 y + 20}{25 - y ^{2}} \cdot \frac{y ^{2} + 5 y}{y ^{2} - 4 y}

What is ((1/(x+1)-1/(x-1)))/((1/(x-1)+1/(x+1))) ?
The solution to ((1/(x+1)-1/(x-1)))/((1/(x-1)+1/(x+1))) is -1/x