\(\dfrac{x}{2x-1}-\dfrac{3x}{2x+1}=5\)
\(\Leftrightarrow\dfrac{x}{2x-1}-\dfrac{3x}{2x+1}-5=0\)
\(\Leftrightarrow\dfrac{x\left(2x+1\right)-3x\left(2x-1\right)-5\left(2x-1\right)\left(2x+1\right)}{\left(2x-1\right)\left(2x+1\right)}=0\)
\(\Leftrightarrow2x^2+x-6x^2+3x-20x^2+5=0\)
\(\Leftrightarrow-24x^2+4x+5=0\)
\(\Delta=b^2-4ac=4^2-4.\left(-24\right).5=496>0\Rightarrow\sqrt{\Delta}=4\sqrt{31}\)
\(\Rightarrow\) Pt có 2 nghiệm pb
\(\left\{{}\begin{matrix}x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-4+4\sqrt{31}}{2.\left(-24\right)}=\dfrac{1+\sqrt{31}}{12}\\x_2=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-4-4\sqrt{31}}{2a}=\dfrac{1-\sqrt{31}}{12}\end{matrix}\right.\)
