`\frac{1}{x²+2x+3} +4 = \frac{1}{x²+1}`
ĐK:$\left \{ {{x²+2x+3≠0} \atop {x²+1≠0}} \right.$ `\,`(luôn đúng)
Pt `<=> \frac{1}{x²+2x+3} = \frac{1}{x²+1}-4`
`<=> \frac{1}{x²+2x+3}= \frac{1-4(x²+1)}{x²+1}`
`<=> \frac{1}{x²+2x+3}= \frac{-4x²-3}{x²+1}` (1)
Ta thấy:
`\frac{1}{x²+2x+3} = \frac{1}{(x+1)²+2} >0 ∀x`
`\frac{-4x²-3}{x²+1} = \frac{-(4x²+3)}{x²+1} <0 ∀x`
`=>` pt (1) vô nghiệm.
Vậy pt vô nghiệm.
