What is expand ((y-xz)(z-xy)(x-yz))/(xyz) ?

The solution to expand ((y-xz)(z-xy)(x-yz))/(xyz) is 1-(yz)/x-(yx)/z+y^2-(xz)/y+z^2+x^2-yxz

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expand ((y-xz)(z-xy)(x-yz))/(xyz)

expand

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

1 - \frac{yz}{x} - \frac{y x}{z} + y^{2} - \frac{x z}{y} + z^{2} + x^{2} - y x z

Solution steps

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

Expand

(y - x z) (z - x y) (x - yz) : y x z - y^{2} z^{2} - y^{2} x^{2} + y^{3} x z - x^{2} z^{2} + y x z^{3} + y x^{3} z - y^{2} x^{2} z^{2}

= \frac{y x z - y ^{2} z ^{2} - y ^{2} x ^{2} + y ^{3} x z - x ^{2} z ^{2} + y x z ^{3} + y x ^{3} z - y ^{2} x ^{2} z ^{2}}{y x z}

Apply the fraction rule:

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

\frac{y x z - y ^{2} z ^{2} - y ^{2} x ^{2} + y ^{3} x z - x ^{2} z ^{2} + y x z ^{3} + y x ^{3} z - y ^{2} x ^{2} z ^{2}}{x yz} = \frac{y x z}{x yz} - \frac{y ^{2} z ^{2}}{x yz} - \frac{y ^{2} x ^{2}}{x yz} + \frac{y ^{3} x z}{x yz} - \frac{x ^{2} z ^{2}}{x yz} + \frac{y x z ^{3}}{x yz} + \frac{y x ^{3} z}{x yz} - \frac{y ^{2} x ^{2} z ^{2}}{x yz}

= \frac{y x z}{y x z} - \frac{y ^{2} z ^{2}}{y x z} - \frac{y ^{2} x ^{2}}{y x z} + \frac{y ^{3} x z}{y x z} - \frac{x ^{2} z ^{2}}{y x z} + \frac{y x z ^{3}}{y x z} + \frac{y x ^{3} z}{y x z} - \frac{y ^{2} x ^{2} z ^{2}}{y x z}

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

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

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

\frac{y ^{3} x z}{x yz} = y^{2}

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

\frac{y x z ^{3}}{x yz} = z^{2}

\frac{y x ^{3} z}{x yz} = x^{2}

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

= 1 - \frac{yz}{x} - \frac{y x}{z} + y^{2} - \frac{x z}{y} + z^{2} + x^{2} - y x z

\frac{a - b ( a - c )}{b + e}

\frac{x}{( x - 8 ) ( x ^{2} + 1 ) ^{3}}

(- 3, 4) y (4, - 6)

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

\frac{( a - b ) ^{2}}{2 ab}

What is expand ((y-xz)(z-xy)(x-yz))/(xyz) ?
The solution to expand ((y-xz)(z-xy)(x-yz))/(xyz) is 1-(yz)/x-(yx)/z+y^2-(xz)/y+z^2+x^2-yxz