\(\dfrac{2x-5}{x^2-4}-\dfrac{3x-2}{x-2}=-17\left(dk:x\ne\pm2\right)\)
\(\Leftrightarrow\dfrac{2x-5}{\left(x-2\right)\left(x+2\right)}-\dfrac{3x-2}{x-2}+17=0\)
\(\Leftrightarrow\dfrac{2x-5-\left(3x-2\right)\left(x+2\right)+17\left(x^2-4\right)}{x^2-4}=0\)
\(\Leftrightarrow2x-5-3x^2-6x+2x+4+17x^2-68=0\)
\(\Leftrightarrow14x^2-2x-69=0\)
\(\Delta=b^2-4ac=\left(-2\right)^2-4.14.\left(-69\right)=3868>0\)
\(\Rightarrow\) Pt có 2 nghiệm pb \(x_1,x_2\)
\(\left\{{}\begin{matrix}x_1=\dfrac{2+\sqrt{3868}}{2.14}=\dfrac{1+\sqrt{967}}{14}\\x_2=\dfrac{2-\sqrt{3868}}{2.14}=\dfrac{1-\sqrt{967}}{14}\end{matrix}\right.\) \(\left(tmdk\right)\)
Vậy ...
\(\dfrac{2x-5}{x^2-4}-\dfrac{3x-2}{x-2}=-17\left(1\right)\)
\(\Leftrightarrow\dfrac{2x-5}{\left(x+2\right)\left(x-2\right)}-\dfrac{3x-2}{x-2}=-17\)
\(ĐKXĐ:\Leftrightarrow\left\{{}\begin{matrix}x+2\ne0\\x-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-2\\x\ne2\end{matrix}\right.\)
\(\Leftrightarrow\dfrac{2x-5}{\left(x+2\right)\left(x-2\right)}-\dfrac{3x-2\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{-17\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\)
\(\Leftrightarrow2x-5-3x-2\left(x+2\right)=-17\left(x+2\right)\left(x-2\right)\)
\(\Leftrightarrow2x-5-3x^2-6x-2x-4=-17x-34-17x+34\)
\(\Leftrightarrow2x-5-3x^2-6x-2x-4+17x+34+17x-34=0\)
\(\Leftrightarrow-3x^2+28x-9=0\)
\(\Leftrightarrow-3x^2+27x+x-9=0\)
\(\Leftrightarrow\left(3x^2-27x\right)+\left(x-9\right)=0\)
\(\Leftrightarrow3x\left(x-9\right)+\left(x-9\right)=0\)
\(\Leftrightarrow\left(x-9\right)+3x=0\)
Vậy ...
