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

The solution to expand ((x+y)(x+z)(y+z))/(xyz) is x/z+y/z+2+y/x+z/x+x/y+z/y

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

expand

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

\frac{x}{z} + \frac{y}{z} + 2 + \frac{y}{x} + \frac{z}{x} + \frac{x}{y} + \frac{z}{y}

Solution steps

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

Expand

(x + y) (x + z) (y + z) : x^{2} y + x y^{2} + 2 x yz + y^{2} z + y z^{2} + x^{2} z + x z^{2}

= \frac{x ^{2} y + x y ^{2} + 2 x yz + y ^{2} z + y z ^{2} + x ^{2} z + x z ^{2}}{x yz}

Apply the fraction rule:

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

\frac{x ^{2} y + x y ^{2} + 2 x yz + y ^{2} z + y z ^{2} + x ^{2} z + x z ^{2}}{x yz} = \frac{x ^{2} y}{x yz} + \frac{x y ^{2}}{x yz} + \frac{2 x yz}{x yz} + \frac{y ^{2} z}{x yz} + \frac{y z ^{2}}{x yz} + \frac{x ^{2} z}{x yz} + \frac{x z ^{2}}{x yz}

= \frac{x ^{2} y}{x yz} + \frac{x y ^{2}}{x yz} + \frac{2 x yz}{x yz} + \frac{y ^{2} z}{x yz} + \frac{y z ^{2}}{x yz} + \frac{x ^{2} z}{x yz} + \frac{x z ^{2}}{x yz}

\frac{x ^{2} y}{x yz} = \frac{x}{z}

\frac{x y ^{2}}{x yz} = \frac{y}{z}

\frac{2 x yz}{x yz} = 2

\frac{y ^{2} z}{x yz} = \frac{y}{x}

\frac{y z ^{2}}{x yz} = \frac{z}{x}

\frac{x ^{2} z}{x yz} = \frac{x}{y}

\frac{x z ^{2}}{x yz} = \frac{z}{y}

= \frac{x}{z} + \frac{y}{z} + 2 + \frac{y}{x} + \frac{z}{x} + \frac{x}{y} + \frac{z}{y}

P (- 5, 2) Q (2, - 1)

\frac{e ^{- 3 s}}{s ( s ^{2} + 9 )}

(5 + 2 i)^{3} + (5 - 2 i)^{3}

3 (2 + 7)

(x y + y^{2}) d x + (x + 2 y - 1) d y

What is expand ((x+y)(x+z)(y+z))/(xyz) ?
The solution to expand ((x+y)(x+z)(y+z))/(xyz) is x/z+y/z+2+y/x+z/x+x/y+z/y