\(a,4x^2-1-x\left(2x-1\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(2x+1\right)-x\left(2x-1\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(2x+1-x\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-1\end{matrix}\right.\\ b,ĐKXĐ:x\ne\pm3\\ \dfrac{x+3}{x-3}+\dfrac{x-3}{x+3}=\dfrac{x^2+2x}{x^2-9}+1\\ \Leftrightarrow\dfrac{\left(x+3\right)^2}{\left(x-3\right)\left(x+3\right)}+\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2+2x}{\left(x-3\right)\left(x+3\right)}+\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(\Leftrightarrow\dfrac{x^2+6x+9}{\left(x-3\right)\left(x+3\right)}+\dfrac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}-\dfrac{x^2+2x}{\left(x-3\right)\left(x+3\right)}-\dfrac{x^2-9}{\left(x-3\right)\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{x^2+6x+9+x^2-6x+9-x^2-2x-x^2+9}{\left(x-3\right)\left(x+3\right)}=0\)
\(\Rightarrow-2x+27=0\\ \Leftrightarrow x=\dfrac{27}{2}\left(tm\right)\)
