What is expand (x+1/y)(y+1/z)(z+1/x) ?

The solution to expand (x+1/y)(y+1/z)(z+1/x) is xyz+y+x+1/z+z+1/x+1/y+1/(yzx)

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expand (x+1/y)(y+1/z)(z+1/x)

expand

(x + \frac{1}{y}) (y + \frac{1}{z}) (z + \frac{1}{x})

x yz + y + x + \frac{1}{z} + z + \frac{1}{x} + \frac{1}{y} + \frac{1}{yz x}

Solution steps

(x + \frac{1}{y}) (y + \frac{1}{z}) (z + \frac{1}{x})

Expand

(x + \frac{1}{y}) (y + \frac{1}{z}) (z + \frac{1}{x}) : (x y + \frac{x}{z} + 1 + \frac{1}{yz}) (z + \frac{1}{x})

= (x y + \frac{x}{z} + 1 + \frac{1}{yz}) (z + \frac{1}{x})

Distribute parentheses

= x yz + x y \frac{1}{x} + \frac{x}{z} z + \frac{x}{z} \cdot \frac{1}{x} + 1 \cdot z + 1 \cdot \frac{1}{x} + \frac{1}{yz} z + \frac{1}{yz} \cdot \frac{1}{x}

Simplify

x yz + x y \frac{1}{x} + \frac{x}{z} z + \frac{x}{z} \cdot \frac{1}{x} + 1 \cdot z + 1 \cdot \frac{1}{x} + \frac{1}{yz} z + \frac{1}{yz} \cdot \frac{1}{x} : x yz + y + x + \frac{1}{z} + z + \frac{1}{x} + \frac{1}{y} + \frac{1}{yz x}

= x yz + y + x + \frac{1}{z} + z + \frac{1}{x} + \frac{1}{y} + \frac{1}{yz x}

+ (x^{2} + y^{2}) d y

6 (\frac{2 x + 4}{3} - \frac{y}{2} = \frac{9}{2})

4 \cdot (\frac{4}{13}) - 2.99 (\frac{3}{13}) - 3 (\frac{3}{13} + \frac{3}{13}) - 3

(1 + \frac{x}{100})^{5}

\frac{2}{k ( k + 1 ) ( k + 2 )}

What is expand (x+1/y)(y+1/z)(z+1/x) ?
The solution to expand (x+1/y)(y+1/z)(z+1/x) is xyz+y+x+1/z+z+1/x+1/y+1/(yzx)