Разложим квадратный трёхчлен на множители, найдя его корни по теореме Виета.
х1=-1, х2=-3
![image](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-1%29%28x%2B1%29%28x%2B3%29%7D%7Bx%5E2%2B2%7D+%5Cgeq+0%5C%5C%5C%5Cx%5E2%2B2%3E0%5C%3B+dlya%5C%3B+x%5Cin+R%5C%3B+%5C%3B+%5Cto+%5C%5C%5C%5C%28x-1%29%28x%2B1%29%28x%2B3%29+%5Cgeq+0%5C%5C%5C%5C%2B+%2B+%2B+%2B%28-3%29-+-+-+%28-1%29%2B+%2B+%2B+%2B%281%29-+-+-+-+-%5C%5C%5C%5Cx%5Cin+%28%5Cinfty%2C-3%5DU%5B-1%2C1%5D)
0\; dlya\; x\in R\; \; \to \\\\(x-1)(x+1)(x+3) \geq 0\\\\+ + + +(-3)- - - (-1)+ + + +(1)- - - - -\\\\x\in (\infty,-3]U[-1,1]" alt="\frac{(x-1)(x+1)(x+3)}{x^2+2} \geq 0\\\\x^2+2>0\; dlya\; x\in R\; \; \to \\\\(x-1)(x+1)(x+3) \geq 0\\\\+ + + +(-3)- - - (-1)+ + + +(1)- - - - -\\\\x\in (\infty,-3]U[-1,1]" align="absmiddle" class="latex-formula">