A=\(\frac{1}{x-1}-\frac{1}{\left(1-x\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}\)
A=\(\frac{\left(x-2\right)\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}+\frac{x-3}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}+\frac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
A= \(\frac{x^2-5x+6}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}+\frac{x-3}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}+\frac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
A= \(\frac{x^2-3x+2}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
A=\(\frac{\left(x-1\right)\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
A=\(\frac{1}{x-3}\)
