\(\dfrac{2}{2x+1}+\dfrac{1}{x+1}=\dfrac{3}{\left(2x+1\right)\left(x+1\right)}\left(x\ne-\dfrac{1}{2};x\ne-1\right)\\ \Leftrightarrow\dfrac{2\left(x+1\right)}{\left(2x+1\right)\left(x+1\right)}+\dfrac{2x+1}{\left(2x+1\right)\left(x+1\right)}=\dfrac{3}{\left(2x+1\right)\left(x+1\right)}\\ \Leftrightarrow2x+2+2x+1=3\\ \Leftrightarrow4x+3=3\\ \Leftrightarrow4x=0\\ \Leftrightarrow x=0\left(tm\right)\)
\(\dfrac{2}{2x+1}+\dfrac{1}{x+1}=\dfrac{3}{\left(2x+1\right)\left(x+1\right)}\) (ĐK:\(x\ne-\dfrac{1}{2};x\ne-1\)
\(\Leftrightarrow\dfrac{2x+2}{\left(2x+1\right)\left(x+1\right)}+\dfrac{2x+1}{\left(2x+1\right)\left(x+1\right)}=\dfrac{3}{\left(2x+1\right)\left(x+1\right)}\)
\(\Leftrightarrow\dfrac{4x+3}{\left(2x+1\right)\left(x+1\right)}=\dfrac{3}{\left(2x+1\right)\left(x+1\right)}\)
\(\Leftrightarrow4x+3=3\)
\(\Leftrightarrow4x=0\)
\(\Leftrightarrow x=0\) (T/m)
