`y=(x-3)/sqrt[x^2+2]`
`y'=\frac{(x-3)'.sqrt[x^2+2]-(x-3).(sqrt[x^2+2])'}{(sqrt[x^2+2])^2}`
`y'=\frac{sqrt[x^2+2]-(x-3).x/(sqrt[x^2+2])}{(sqrt[x^2+2])^2}`
`y'=\frac{(x^2+2-x^2+3x)/(sqrt[x^2+2])}{(sqrt[x^2+2])^2}`
`y'=\frac{2+3x}{(sqrt[x^2+2])^3`
`y'>0`
`⇔2+3x>0` `((sqrt[x^2+2])^3>0,∀x)`
`⇔x> (-2)/3`