To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $6\left(x-3\right)\left(x-2\right)$ and $\left(x-3\right)\left(-x+1\right)$ is $6\left(x-3\right)\left(x-2\right)\left(-x+1\right)$. Multiply $\frac{1}{6\left(x-3\right)\left(x-2\right)}$ times $\frac{-x+1}{-x+1}$. Multiply $\frac{2}{\left(x-3\right)\left(-x+1\right)}$ times $\frac{6\left(x-2\right)}{6\left(x-2\right)}$.
Since $\frac{-x+1}{6\left(x-3\right)\left(x-2\right)\left(-x+1\right)}$ and $\frac{2\times 6\left(x-2\right)}{6\left(x-3\right)\left(x-2\right)\left(-x+1\right)}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $6\left(x-3\right)\left(x-2\right)\left(-x+1\right)$ and $\left(x-2\right)\left(x-1\right)$ is $6\left(x-3\right)\left(x-2\right)\left(x-1\right)$. Multiply $\frac{11x-23}{6\left(x-3\right)\left(x-2\right)\left(-x+1\right)}$ times $\frac{-1}{-1}$. Multiply $\frac{3}{\left(x-2\right)\left(x-1\right)}$ times $\frac{6\left(x-3\right)}{6\left(x-3\right)}$.
Since $\frac{-\left(11x-23\right)}{6\left(x-3\right)\left(x-2\right)\left(x-1\right)}$ and $\frac{3\times 6\left(x-3\right)}{6\left(x-3\right)\left(x-2\right)\left(x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.
