c) \(\dfrac{12x+1}{6x-2}-\dfrac{9x-5}{3x+1}=\dfrac{108x-36x^2-9}{4\left(9x^2-1\right)}\) (ĐK:\(x\ne\pm\dfrac{1}{3}\))
\(\Leftrightarrow\dfrac{\left(12x+1\right)\left(3x+1\right)}{2\left(3x-1\right)\left(3x+1\right)}-\dfrac{2\left(9x-5\right)\left(3x-1\right)}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{-9\left(4x^2-12x+1\right)}{4\left(9x^2-1\right)}\)
\(\Leftrightarrow\dfrac{36x^2+15x+1-54x^2+48x-10}{2\left(9x^2-1\right)}=\dfrac{-9\left(4x^2-12x+1\right)}{4\left(9x^2-1\right)}\)
\(\Leftrightarrow\dfrac{-18x^2+63x-9}{2\left(9x^2-1\right)}=\dfrac{-9\left(4x^2-12x+1\right)}{4\left(9x^2-1\right)}\)
\(\Leftrightarrow-36x^2+126x-18=-36x^2+108x-9\)
\(\Leftrightarrow18x=9\Leftrightarrow x=\dfrac{1}{2}\) (T/m)
d) \(\dfrac{x+4}{x^2-3x+2}+\dfrac{x+1}{x^2-4x+3}=\dfrac{2x+5}{x^2-4x+3}\) (ĐK:\(x\ne1;x\ne2;x\ne3\) )
\(\Leftrightarrow\dfrac{x+4}{\left(x-1\right)\left(x-2\right)}+\dfrac{x+1}{\left(x-1\right)\left(x-3\right)}=\dfrac{2x+5}{\left(x-1\right)\left(x-3\right)}\)
\(\Leftrightarrow\dfrac{x+4}{\left(x-1\right)\left(x-2\right)}-\dfrac{x+4}{\left(x-1\right)\left(x-3\right)}=0\)
\(\Leftrightarrow\dfrac{\left(x+4\right)\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}-\dfrac{\left(x+4\right)\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=0\)
\(\Leftrightarrow\left(x+4\right)\left(x-3-x+2\right)=0\)
\(\Leftrightarrow x=-4\) (T/m)
