Question

resolva a inequaçao quociente: x+3/x-1≥0

Answer 1

Resolver a inequação do tipo quociente

$\mathtt{\dfrac{x+3}{x-1}\geq 0}\quad\quad\texttt{com }x\ne 1}$


Para o numerador temos

$\mathtt{x+3 \geq 0}\\\\ \mathtt{x \geq -3}$


Para o denominador temos

$\mathtt{x-1 \geq 0}\\\\ \mathtt{x \geq 1}$


Fazendo a análise dos sinais

$\begin{array}{cc} \mathtt{N}~&~\mathtt{\underline{----}\underset{-3}\bullet \underline{++++++++}} \end{array}\\\\ \begin{array}{cc} \mathtt{D}~&~\mathtt{\underline{--------}\underset{1}{\circ}\underline{++++}} \end{array}\\\\\\ \begin{array}{cc} \mathtt{Q}~&~\mathtt{\underline{++++}\underset{-3}\bullet \underline{---}\underset{1}{\circ} \underline{++++}} \end{array}$


Conjunto solução:  $\mathtt{S=]-\infty ,-3]~\cup ~]1,+\infty[}$


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