ĐKXĐ:\(x\ne\pm1\)
\(\dfrac{4x+5}{x-1}+\dfrac{2x-1}{x+1}=6\\ \Leftrightarrow\dfrac{\left(x+1\right)\left(4x+5\right)}{\left(x+1\right)\left(x-1\right)}+\dfrac{\left(x-1\right)\left(2x-1\right)}{\left(x+1\right)\left(x-1\right)}=6\\ \Leftrightarrow\dfrac{\left(x+1\right)\left(4x+5\right)+\left(x-1\right)\left(2x-1\right)}{\left(x+1\right)\left(x-1\right)}=6\)
\(\Leftrightarrow4x^2+4x+5x+5+2x^2-2x-x+1=6\left(x^2-1\right)\\ \Leftrightarrow6x^2+6x+6=6x^2-6\\ \Leftrightarrow6x=-12\\ \Leftrightarrow x=-2\left(tm\right)\)
\(\dfrac{4x+5}{x-1}+\dfrac{2x-1}{x+1}=6\)
\(\dfrac{\left(4x+5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\dfrac{\left(2x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{\left(4x+5\right)\left(x+1\right)+\left(2x-1\right)\left(x-1\right)}{x^2-1}\)
\(\dfrac{4x^2+9x+5+2x^2-3x+1}{x^2-1}=\dfrac{6x^2+6x+6}{x^2-1}=6\)
\(\Rightarrow6x^2+6x+6=6\left(x^2-1\right)=6x^2-6\)
\(\Rightarrow6x+12=0\Rightarrow x=-2\)