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

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

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

simplify

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

x - 1

Solution steps

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

Apply rule:

(a) = a

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Factor

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

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

Cancel the common factor:

x + 1

= x - 1

(6 y - 5) (4 y^{3} - 5 y^{2} - 3 x + 4)

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

f (n) = \frac{2 ^{n}}{4 ^{n}}

5 - 2 (\frac{3}{4})^{2}

(x - \frac{1}{2})^{6}