Question

Inecuación Cuadrática

x²+ 2x +3 < x+2
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x+1

Answer 1

$\dfrac{x^2+2x+3}{x+1}\ \textless \ x+2\\ \\ \\ \dfrac{x^2+2x+3}{x+1}-(x+2)\ \textless \ 0\\ \\ \\ \dfrac{(x^2+2x+3)-(x+1)(x+2)}{x+1}\ \textless \ 0\\ \\ \\ \dfrac{-x+1}{x+1}\ \textless \ 0\\ \\ \\ \dfrac{x-1}{x+1}\ \textgreater \ 0\\ \\ \\ (x-1)(x+1)\ \textgreater \ 0\\ \\ \boxed{x\in (-\infty,-1)\cup(1,+\infty)}$