a) Để biểu thức có nghĩa
\(\Leftrightarrow\dfrac{3}{2}x-\dfrac{9}{4}\ge0\)
\(\Leftrightarrow\dfrac{3}{2}x\ge\dfrac{9}{4}\)
\(\Leftrightarrow x\ge\dfrac{3}{2}\)
b) Để biểu thức có nghĩa
\(\Leftrightarrow\dfrac{5}{5-3x}\ge0\)
\(\Leftrightarrow5-3x>0\) (Vì 5 > 0)
\(\Leftrightarrow-3x>-5\)
\(\Leftrightarrow3x< 5\)
\(\Leftrightarrow x< \dfrac{5}{3}\)
c) Để biểu thức có nghĩa
\(\Leftrightarrow\dfrac{3}{4-x^2}\ge0\)
\(\Leftrightarrow4-x^2>0\) (Vì 3 > 0)
\(\Leftrightarrow-x^2>-4\)
\(\Leftrightarrow x^2< 4\)
\(\Leftrightarrow x< -2\)
d) Để biểu thức có nghĩa thì
\(x^2+3x+2\ge0\)
\(\Leftrightarrow x^2+2x+x+2\ge0\)
\(\Leftrightarrow x\left(x+2\right)+\left(x+2\right)\ge0\)
\(\Leftrightarrow\left(x+1\right)\left(x+2\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x+2< 0\end{matrix}\right.\\x+1=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x>-2\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x< -2\end{matrix}\right.\\x=-1\\x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>-1\\x< -2\\x=-1\\x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge-1\\x\le-2\end{matrix}\right.\)
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