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\frac{\left(x-y\right)z}{xyz}+\frac{\left(y-z\right)x}{xyz}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of xy and yz is xyz. Multiply \frac{x-y}{xy} times \frac{z}{z}. Multiply \frac{y-z}{yz} times \frac{x}{x}.
\frac{\left(x-y\right)z+\left(y-z\right)x}{xyz}
Since \frac{\left(x-y\right)z}{xyz} and \frac{\left(y-z\right)x}{xyz} have the same denominator, add them by adding their numerators.
\frac{xz-yz+yx-zx}{xyz}
Do the multiplications in \left(x-y\right)z+\left(y-z\right)x.
\frac{-yz+yx}{xyz}
Combine like terms in xz-yz+yx-zx.
\frac{y\left(x-z\right)}{xyz}
Factor the expressions that are not already factored in \frac{-yz+yx}{xyz}.
\frac{x-z}{xz}
Cancel out y in both numerator and denominator.
\frac{\left(x-y\right)z}{xyz}+\frac{\left(y-z\right)x}{xyz}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of xy and yz is xyz. Multiply \frac{x-y}{xy} times \frac{z}{z}. Multiply \frac{y-z}{yz} times \frac{x}{x}.
\frac{\left(x-y\right)z+\left(y-z\right)x}{xyz}
Since \frac{\left(x-y\right)z}{xyz} and \frac{\left(y-z\right)x}{xyz} have the same denominator, add them by adding their numerators.
\frac{xz-yz+yx-zx}{xyz}
Do the multiplications in \left(x-y\right)z+\left(y-z\right)x.
\frac{-yz+yx}{xyz}
Combine like terms in xz-yz+yx-zx.
\frac{y\left(x-z\right)}{xyz}
Factor the expressions that are not already factored in \frac{-yz+yx}{xyz}.
\frac{x-z}{xz}
Cancel out y in both numerator and denominator.