A) \[(-2,-1)\]
B) \[\left( \frac{-5-\sqrt{13}}{2},\frac{-5+\sqrt{13}}{2} \right)\]
C) \[\left( -\,2,\infty \right)\]
D) \[(-1,\ \infty )\]
Correct Answer: A
Solution :
(a): \[\frac{{{x}^{2}}+5x+3}{x+2}<x\Rightarrow \frac{{{x}^{2}}+5x+3}{x+2}-x<0\] \[\Rightarrow \frac{{{x}^{2}}+5x+3-{{x}^{2}}-2x}{x+2}<0\] \[\Rightarrow \frac{3x+3}{x+2}<0\Rightarrow \frac{x+1}{x+2}<0\] We know that \[\left( x-\alpha \right)\left( x-\beta \right)<0\] \[\Rightarrow \alpha <x<\beta \] where \[\left( \alpha <\beta \right)\] \[\therefore -2<x<-1\]
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