Bonjour,
[tex] \dfrac{3x-4}{x+1} \leq \dfrac{x-1}{2x+3} \\
\ \textless \ ==\ \textgreater \ \dfrac{3x-4}{x+1} - \dfrac{x-1}{2x+3}\leq 0\\
\ \textless \ ==\ \textgreater \ \dfrac{(3x-4)(2x+3)}{(x+1)(2x+3)} - \dfrac{(x-1)(x+1)}{(2x+3)(x+1)}\leq 0\\
\ \textless \ ==\ \textgreater \ \dfrac{5x^2+x-11}{(x+1)(2x+3)}\leq 0\\
[/tex]
[tex]A=5x^2+x-11\\ B=2x^2+5x+3\\ f(x)= \dfrac{A}{B} \\
u=\frac{-1- \sqrt{221}}{10}\\
v=\frac{-1+\sqrt{221}}{10}\\
[/tex]
[tex]\begin{array}{|c|ccccccccccc|}x&-\infty&&u&& -\frac{3}{2}&&-1&&v&&+\infty\\A&&+&0&-&-&-&-&-&0&+&\\B&&+&+&+&0&-&0&+&+&+&\\
f(x)&&+&0&-&|&+&|&-&0&+& \end{array}
[/tex]
u<=x<-3/2 ou -1<x<=v
