To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x+y-z\right)\left(x-y+z\right)$ and $\left(x+y-z\right)\left(-x+y+z\right)$ is $\left(x+y-z\right)\left(x-y+z\right)\left(-x+y+z\right)$. Multiply $\frac{y-z}{\left(x+y-z\right)\left(x-y+z\right)}$ times $\frac{-x+y+z}{-x+y+z}$. Multiply $\frac{z-x}{\left(x+y-z\right)\left(-x+y+z\right)}$ times $\frac{x-y+z}{x-y+z}$.
Since $\frac{\left(y-z\right)\left(-x+y+z\right)}{\left(x+y-z\right)\left(x-y+z\right)\left(-x+y+z\right)}$ and $\frac{\left(z-x\right)\left(x-y+z\right)}{\left(x+y-z\right)\left(x-y+z\right)\left(-x+y+z\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{-x+y}{\left(x-y+z\right)\left(-x+y+z\right)}$ and $\frac{x-y}{\left(x-y+z\right)\left(-x+y+z\right)}$ have the same denominator, add them by adding their numerators.
