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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

x

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

2 (11 - 7)

1 + cos (x) (1 - cos (x))

(x - 2) (x - 5) (x - 3) (x + 3)

(x^{\frac{1}{3}} + 3)^{2}

- \frac{5 z - 8}{3 ( 8 + 5 z )}

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