What is \frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)} equal to?

Explanation

Taking the LCM as xyz(x-y)(y-z)(z-x), the numerator simplifies to -yz(y-z) - zx(z-x) - xy(x-y), which equals (x-y)(y-z)(z-x). Dividing this by the denominator leaves \frac{1}{xyz}.

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