Respuesta :

[tex]\begin{gathered} x-1=\frac{x^2-4x+3}{x+2} \\ \Rightarrow\frac{x-1}{1}=\frac{x^2-4x+3}{x+2} \\ \text{Cross multiplying} \\ \Rightarrow x^2-4x+3=(x-1)(x+2) \\ =x(x+2)-1(x+2) \\ =x^2+2x-x-2 \\ =x^2+x-2 \end{gathered}[/tex]

That is

[tex]\begin{gathered} x^2-4x+3=x^2+x-2 \\ \Rightarrow x^2-4x+3-x^2-x+2=0 \\ \text{Collecting like terms, we have:} \\ x^2-x^2-4x-x+3+2=0 \\ -5x+5=0 \\ -5x=-5 \\ \frac{-5x}{-5}=\frac{-5}{-5} \\ x=1 \end{gathered}[/tex]

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