Solve the Inequalities

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A. [tex]\frac{ x^{2 }-3x+1 }{1-x}[/tex] <0 [tex]\Leftrightarrow[/tex] ([tex]x^{2 }[/tex]-3x+1)(1-x) <0

[tex]\begin{array}{|l} x^{2 } -3x + 1 >0\\ 1-x <0 \end{array}[/tex] or

[tex]\begin{array}{|l} x^{2 }-3 x + 1 <0\\ 1-x > 0 \end{array}[/tex]

[tex]\begin{array}{|l} x \in( - \infty ; \frac{3- \sqrt{5} }{2} ) \cup ( \frac{3+ \sqrt{5} }{2} ; + \infty) \\ x >1\end{array}[/tex] or

[tex]\begin{array}{|l} x \in ( \frac{3- \sqrt{5} }{2} ; \frac{3+ \sqrt{5} }{2} )\\ x <1 \end{array}[/tex]

1 case x[tex]\in( \frac{3+ \sqrt{5} }{2} ; + \infty )[/tex]

2 case x[tex]\in( \frac{3- \sqrt{5} }{2} ;1)[/tex]