[tex] Bonjour; \\\\\\ \dfrac{x-1}{2x-5} = \dfrac{x+1}{x-1} \Longrightarrow \dfrac{(x-1)^2}{(x-1)(2x-5)} = \dfrac{(x+1)(2x-5)}{(x-1)(2x-5)} \\\\\\ \Longrightarrow (x - 1)^2 = (x +1)(2x-5) \\\\\\ \Longrightarrow x^2 - 2x + 1 = 2x^2 - 5x + 2x - 5 = 2x^2 - 3x - 5 \\\\\\ \Longrightarrow 0 = x^2 - x - 6 = x^2 - 3x + 2x - 6 = x(x-3) + 2(x-3) \\\\\\ = (x - 3)(x + 2) \Longrightarrow x = 3 \ ou \ x = - 2 \ . [/tex]
Bonjour,
[tex] \frac{x-1}{2x-5}=\frac{x+1}{x-1}\\\\
\frac{(x-1)(2x-5)(x-1)}{(2x-5)} =\frac{(x+1)(2x-5)(x-1)}{x-1} \\\\
(x-1)(x-1)=(x+1)(2x-5)\\\\
(x-1)(x-1)-(x+1)(2x-5)=0\\\\
-x^2+x+6=0\\\\
\Delta=1^2-4\times (-1)\times 6=25>0\\\\
x_1=\frac{-1-\sqrt{25}}{-2}=3\\\\
x_2=\frac{-1+\sqrt{25}}{-2}=-2
[/tex]
