\(\dfrac{x-1}{x+3}-\dfrac{7}{x-2}=\dfrac{x^2+6}{\left(x+3\right)\left(x-2\right)}\\ ĐKXĐ:x\ne-3;x\ne2\\ \Leftrightarrow\dfrac{\left(x-1\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\dfrac{7\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=\dfrac{x^2+6}{\left(x+3\right)\left(x-2\right)}\\ \Leftrightarrow x^2-2x-x+2-7x-21=x^2+6\\ \Leftrightarrow x^2-2x-x-7x-x^2=6-2+21\\ \Leftrightarrow-10x=25\\ \Leftrightarrow x=-\dfrac{25}{10}=-\dfrac{5}{2}\left(nhận\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)-7\left(x+3\right)=x^2+6\)
\(\Leftrightarrow x^2-3x+2-7x-21=x^2+6\)
=>-10x-19=6
=>-10x=25
hay x=-5/2
\(\Rightarrow\left(x-1\right).\left(x-2\right)-7x-21=x^2+6\)
\(\Rightarrow x^2-3x+2-7x-21=6+x^2\)
\(\Rightarrow-10x-19=6\)
\(\Rightarrow-10x=19+6=25\)
\(\Rightarrow x=\dfrac{25}{-10}=-\dfrac{5}{2}\)
\(\dfrac{\left(x+1\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\dfrac{7\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\dfrac{x^2+6}{\left(x+3\right)\left(x-2\right)}\)
\(\left(x+1\right)\left(x-2\right)-7\left(x+3\right)=x^2+6\)
\(x^2-2x+x-2-7x-21=x^2+6\)
\(x^2-2x+x-2-7x-21-x^2-6=0\)
\(\left(x^2-x^2\right)+\left(-2x-7x+x\right)+\left(-2-21-6\right)=0\)
\(-8x-29=0\)
\(-8x=29\)
\(x=\dfrac{-29}{8}\)
