ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(\dfrac{x+2}{x+3}-1< \dfrac{x+1}{3-x}\)
=>\(\dfrac{x+2-x-3}{x+3}-\dfrac{x+1}{3-x}< 0\)
=>\(-\dfrac{1}{x+3}-\dfrac{x+1}{3-x}< 0\)
=>\(\dfrac{-1}{x+3}+\dfrac{x+1}{x-3}< 0\)
=>\(\dfrac{-x+3+\left(x+1\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}< 0\)
=>\(\dfrac{-x+3+x^2+4x+3}{\left(x+3\right)\left(x-3\right)}< 0\)
=>\(\dfrac{x^2+3x+6}{x^2-9}< 0\)
mà \(x^2+3x+6>0\forall x\)
nên (x-3)(x+3)<0
=>-3<x<3
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