\(\dfrac{3x-1}{x+2}-\dfrac{2x-5}{x-3}=-\dfrac{5}{\left(x+2\right)\left(x-3\right)}\)
ĐKXĐ: \(x\ne-1;x\ne3.\)
\(\dfrac{3x-1}{x+2}-\dfrac{2x-5}{x-3}=-\dfrac{5}{\left(x+2\right)\left(x-3\right)}\)
\(\Leftrightarrow\dfrac{\left(3x-1\right)\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}-\dfrac{\left(2x-5\right)\left(x+2\right)}{\left(x+2\right)\left(x-3\right)}=-\dfrac{5}{\left(x+2\right)\left(x-3\right)}\)
\(\Leftrightarrow\left(3x-1\right)\left(x-3\right)-\left(2x-5\right)\left(x+2\right)=-5\)
\(\Leftrightarrow3x^2-9x-x+3-2x^2-4x+5x+10=-5\)
\(\Leftrightarrow x^2-9x+18=0\)
\(\Leftrightarrow\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{9}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{9}{2}\right)^2-\left(\dfrac{3}{2}\right)^2=0\)
\(\Leftrightarrow\left(x-\dfrac{9}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{9}{2}+\dfrac{3}{2}\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x-3=0\end{matrix}\right.\left[{}\begin{matrix}x=6\\x=3\left(l\right)\end{matrix}\right.\)
đkxđ x\(\ne\)3 x\(\ne\) -2 \(\dfrac{3x-1}{x+2}-\dfrac{2x-5}{x-3}=-\dfrac{5}{\left(x+2\right)\times\left(x-3\right)}\) =\(\dfrac{\left(3x-1\right)\times\left(x-3\right)}{\left(x+2\right)\times_{ }\left(x-3\right)}-\dfrac{\left(2x-5\right)\times\left(x+2\right)}{\left(x+2\right)\times\left(x-3\right)}\)=\(\dfrac{-5}{\left(x+2\right)\times\left(x-3\right)}\) =\(\dfrac{3x^2-9x-x+3-\left(2x^2+4x-5x-10\right)}{\left(x+2\times\right)\left(x-3\right)}=\dfrac{-5}{\left(x+2\right)\times\left(x-3\right)}\) =\(\dfrac{3x^2-10x+3-2x^2-4x+5x+10}{\left(x+2\right)\times\left(x-3\right)}=\dfrac{-5}{\left(x+2\right)\times\left(x-3\right)}\) \(\Leftrightarrow\)\(x^2-9x+13=-5\) =x\(^2\) -9x+13+5=o =x\(^2\)-9x+18=0 =x\(^2\)-2\(\times\)9x\(\dfrac{9}{2}\)+\(\left(\dfrac{9}{2}\right)^2\)\(-\dfrac{9}{4}=0\) =\(\left(x-\dfrac{9}{2}\right)^2-\dfrac{9}{4}=0\) =\(\left(x-\dfrac{9}{2}-\dfrac{3}{2}\right)\times\left(x-\dfrac{9}{2}+\dfrac{3}{2}\right)\) =\(\left(x-3\right)\times\left(x-6\right)=0\) =\(\left\{{}\begin{matrix}x=3\left(loại\right)\\x=6\left(chọn\right)\end{matrix}\right.\)
