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

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

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

simplify

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

x - 1

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel the common factor:

x

= x - 1

(e^{x} - e^{- x}) (e^{x} + e^{- x})

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

(1 + sin (2 x))^{2}

(\frac{2}{3} x - \frac{3}{5} y) (\frac{2}{3} x + \frac{3}{5} y)

(1 - cos (t))^{2} + (sin (t))^{2}