\(\dfrac{x+1}{x-1}-\dfrac{x-2}{x-3}=3\) (ĐK: \(x\ne1;x\ne-3\))
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\dfrac{\left(x-2\right)\left(x-1\right)}{\left(x+3\right)\left(x-1\right)}=3\)
\(\Leftrightarrow\dfrac{\left(x^2+x+3x+3\right)-\left(x^2-x-2x+2\right)}{\left(x+3\right)\left(x-1\right)}=3\)
\(\Leftrightarrow\dfrac{x^2+x+3x+3-x^2+x+2x-2}{\left(x+3\right)\left(x-1\right)}=3\)
\(\Leftrightarrow7x+1=3\left(x^2-x+3x-3\right)\)
\(\Leftrightarrow3x^2+6x-9-7x-1=0\)
\(\Leftrightarrow3x^2-x-10=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\3x=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{5}{3}\end{matrix}\right.\)
