Exercício sobre inequações

Resolver em $\,{\rm I\!R}\,$ as inequaçoes abaixo

$\,\dfrac{\;2x\,+\,1\;}{\;x\,+\,2\;}\;\gt\;0\,$

$\,\dfrac{\;3x\,-\,2\;}{\;3\,-\,2x\;}\;\lt\;0\,$

$\,\dfrac{\;3\,-\,4x\;}{\;5x\,+\,1\;}\;\geqslant\;0\,$

$\,\dfrac{\;-3\,-\,2x\;}{\;3x\,+\,1\;}\;\leqslant\;0\,$

resposta: a)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,-2\phantom{X}{\text ou}\phantom{X}x\,\gt\,-\frac{\,1\,}{2}\rbrace\;$ b)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\lt\,\frac{\,2\,}{3}\phantom{X}{\text ou}\phantom{X}x\,\gt\,\frac{\,3\,}{2}\rbrace\;$ c)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;-\frac{\,1\,}{5}\,\lt\,x\,\leqslant\,\frac{\,3\,}{4}\rbrace\;$ d)$\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{\,3\,}{2}\phantom{X}{\text ou}\phantom{X}x\,\gt\,-\frac{\,1\,}{3}\rbrace\;$
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Resolver em $\,{\rm I\!R}\,$ a inequação $\phantom{X}\dfrac{\;3x\,+\,4\;}{1\,-\,x}\phantom{X}$

resposta: $\,\mathbb{S}\;=\;\lbrace x\,\in\,{\rm I\!R}\;|\;x\,\leqslant\,-\frac{2}{5}\phantom{X}{\text e}\phantom{X}x\,\gt\,1\rbrace\;$
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