a) ĐK: \(x\ne\pm\dfrac{3}{2}\)
BPT \(\Leftrightarrow\dfrac{1}{\left|2x-3\right|}>\dfrac{1}{\left|2x+3\right|}\) \(\Rightarrow\left|2x-3\right|< \left|2x+3\right|\)
\(\Leftrightarrow4x^2-12x+9< 4x^2+12x+9\)
\(\Leftrightarrow-24x< 0\) \(\Leftrightarrow x>0\)
Vậy \(x\in\left(0;+\infty\right)\backslash\left\{\dfrac{3}{2}\right\}\)
b) ĐK: \(x\ne1;\dfrac{1}{3}\)
BPT \(\Leftrightarrow\dfrac{9}{x^2-2x+1}\le\dfrac{81}{1-6x+9x^2}\)
\(\Rightarrow9x^2-18x+9\ge1-6x+9x^2\)
\(\Leftrightarrow-12x\ge-8\) \(\Leftrightarrow x\le\dfrac{2}{3}\)
Vậy \(x\in(-\infty;\dfrac{2}{3}]\backslash\left\{\dfrac{1}{3}\right\}\)
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