bạn làm tắt thể khó kiểm
\(\dfrac{2}{x-3}+\dfrac{5}{x+1}=\dfrac{2x}{\left(x+1\right)\left(x+3\right)}\)
\(\dfrac{\left(2x+2\right)+\left(5x-15\right)}{\left(x-3\right)\left(x+1\right)}=\dfrac{7x-13}{\left(x-3\right)\left(x+1\right)}\)
\(\dfrac{\left(7x-13\right)\left(x+3\right)}{\left(x-3\right)\left(x+1\right)}=\dfrac{2x\left(x-3\right)}{MSC}\)
\(\left(đk\right)\left\{{}\begin{matrix}x\ne+-3\\x\ne-1\end{matrix}\right.\Leftrightarrow7x^2+8x-39=2x^2-6x\)
\(5x^2+14x-39=0\)
\(\left(x+\dfrac{7}{5}\right)^2=\dfrac{39}{5}+\dfrac{49}{25}=\dfrac{39.5+49}{5^2}=\dfrac{244}{5^2}\)
\(\left\{{}\begin{matrix}x=\dfrac{-7-2\sqrt{61}}{5}\\x=\dfrac{-7+4\sqrt{61}}{5}\end{matrix}\right.\) Kết luận không vô nghiệm
