ĐKXĐ: \(x\ne\left\{-2;-\dfrac{1}{2};2\right\}\)
\(pt\Leftrightarrow\dfrac{2x+1}{\left(x+2\right)\left(2x+1\right)}-\dfrac{3}{\left(x-2\right)\left(x+2\right)}=2\)
\(\Leftrightarrow\dfrac{1}{x+2}-\dfrac{3}{\left(x-2\right)\left(x+2\right)}=2\)
\(\Leftrightarrow\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}-\dfrac{3}{\left(x-2\right)\left(x+2\right)}=\dfrac{2\left(x^2-4\right)}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow x-5=2\left(x^2-4\right)\)
\(\Leftrightarrow2x^2-x-3=0\Rightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{3}{2}\end{matrix}\right.\)
ĐKXĐ : \(x\notin\left\{-\dfrac{1}{2};2;-2\right\}\)
\(\dfrac{2x+1}{2x^2+5x+2}-\dfrac{3}{x^2-4}=2\\ \Leftrightarrow\dfrac{2x+1}{\left(x+2\right)\left(2x+1\right)}-\dfrac{3}{\left(x-2\right)\left(x+2\right)}=2\\ \Leftrightarrow\dfrac{\left(2x+1\right)\left(x-2\right)-3\left(2x+1\right)}{\left(x-2\right)\left(x+2\right)\left(2x+1\right)}=2\\ \Leftrightarrow2x^2-9x-5=2\left(x^2-4\right)\left(2x+1\right)\\ \Leftrightarrow2x^2-9x-5=4x^3+2x^2-16x-8\\ \Leftrightarrow4x^3-7x-3=0\\ \Leftrightarrow\left(x+1\right)\left(2x-3\right)\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\left(t.m\right)\\x=\dfrac{3}{2}\left(t.m\right)\\x=-\dfrac{1}{2}\left(loai\right)\end{matrix}\right.\)
