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{\frac{x^2-2x+3}{x^2-4x+3}}\geq {0}

Solve the inequality (-2x+3+x^2)/(-4x+3+x^2)%0

Answer

$\frac{\left(x-1\right)^2+2}{\left(x-1\right)\left(x-3\right)}\geq 0$

Step-by-step explanation

Problem

${\frac{x^2-2x+3}{x^2-4x+3}}\geq {0}$
1

Factor the trinomial $3-4x+x^2$ finding two numbers that multiply to form $3$ and added form $-4$

$\begin{matrix}\left(-3\right)\left(-1\right)=3\\ \left(-3\right)+\left(-1\right)=-4\end{matrix}$

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Answer

$\frac{\left(x-1\right)^2+2}{\left(x-1\right)\left(x-3\right)}\geq 0$