b. $$ \frac{2}{x-3}-\frac{x+1}{x^{2}-4 x+3} $$

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Calculate or simplify the expression $$ 2/(x-3)-((x+1)/(x^2-4*x+3)) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{2}{\left(x-3\right)}-\left(\frac{\left(x+1\right)}{\left(x^{2}-4x+3\right)}\right)$$
- step1: Remove the parentheses:
  $$\frac{2}{x-3}-\left(\frac{x+1}{x^{2}-4x+3}\right)$$
- step2: Remove the parentheses:
  $$\frac{2}{x-3}-\frac{x+1}{x^{2}-4x+3}$$
- step3: Factor the expression:
  $$\frac{2}{x-3}-\frac{x+1}{\left(x-1\right)\left(x-3\right)}$$
- step4: Reduce fractions to a common denominator:
  $$\frac{2\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{x+1}{\left(x-1\right)\left(x-3\right)}$$
- step5: Rewrite the expression:
  $$\frac{2\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}-\frac{x+1}{\left(x-1\right)\left(x-3\right)}$$
- step6: Transform the expression:
  $$\frac{2\left(x-1\right)-\left(x+1\right)}{\left(x-1\right)\left(x-3\right)}$$
- step7: Multiply the terms:
  $$\frac{2x-2-\left(x+1\right)}{\left(x-1\right)\left(x-3\right)}$$
- step8: Subtract the terms:
  $$\frac{x-3}{\left(x-1\right)\left(x-3\right)}$$
- step9: Reduce the fraction:
  $$\frac{1}{x-1}$$
La simplification de l'expression donnée est $$ \frac{1}{x-1} $$.
$$ \frac{1}{x-1} $$

b. \( \frac{2}{x-3}-\frac{x+1}{x^{2}-4 x+3} \)

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