a) \(\dfrac{1}{\left(2x-3\right)^2}+\dfrac{3}{\left(2x-3\right)\left(2x+3\right)}+\dfrac{2}{\left(2x+3\right)^2}=0\left(Đk:x\ne\pm\dfrac{2}{3}\right)\)
\(\Leftrightarrow\left(\dfrac{1}{2x-3}+\dfrac{1}{2x+3}\right)\left(\dfrac{1}{2x-3}+\dfrac{2}{2x+3}\right)=0\)
+) \(\dfrac{1}{2x-3}=-\dfrac{1}{2x+3}\)
\(\Leftrightarrow2x+3=3-2x\)
\(\Leftrightarrow x=0\)
+) \(\dfrac{1}{2x-3}=-\dfrac{2}{2x+3}\)
\(\Leftrightarrow2x+3=2\left(3-2x\right)\)
\(\Leftrightarrow x=\dfrac{1}{2}\)
b) \(1+\dfrac{14}{\left(x-4\right)^2}=-\dfrac{9}{x-4}\left(Đk:x\ne4\right)\)
\(\left(x-4\right)^2+14+9\left(x-4\right)=0\)
\(x^2-8x+16+14+9x-36=0\)
\(x^2+x-6=0\)
\(\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
c) \(\dfrac{1+8x}{1+2x}-\dfrac{2x}{2x-1}+\dfrac{12x^2-9}{1-4x^2}=0\left(Đk:x\ne\pm\dfrac{1}{2}\right)\)
\(\left(1+8x\right)\left(1-2x\right)+2x\left(1+2x\right)+12x^2-9=0\)
\(1-2x+8x-16x^2+2x+4x^2+12x^2-9=0\)
\(8x-8=0\)
\(x=1\)
d) \(\dfrac{1}{2\left(x-3\right)}-\dfrac{3x-5}{\left(x-1\right)\left(x-3\right)}=\dfrac{1}{2}\left(Đk:x\ne1;x\ne3\right)\)
\(x-1+2\left(5-3x\right)=x^2-4x+3\)
\(9-5x=x^2-4x+3\)
\(x^2+x-6=0\)
\(\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
