`#Kenshiro`
`a ) M = (3-4x)/(x^2+1)`
`⇔ M = (4x^2 + 4 - 4x -1)/(x^2 + 1)`
`⇔ M = (4(x^2 + 1) - (4x^2 + 4x + 1))/(x^2 + 1 )`
`⇔ M = (4(x^2 + 1) - (2x - 1)^2)/(x^2 + 1)`
`⇔ 4 - ((2x + 1)^2)/(x^2 + 1)`
Ta có :
`(2x + 1)^2 ≥ 0 ∀ x`
`x^2 + 1 > 0 ∀ x`
`⇒ ((2x + 1)^2)/(x^2 + 1) ≥ 0 ∀ x`
`⇒ 4 - ((2x + 1)^2)/(x^2 + 1) ≤ 4 ∀ x`