lean_workbook_plus_56059

Firstly, we have the inequality: $\frac{x}{{x + 1}} \ge \frac{x}{{\sqrt {{x^4} + 3} }} \Leftrightarrow {x^4} + 3 \ge {(x + 1)^2} \Leftrightarrow {(x - 1)^2}({x^2} + 2x + 2) \ge 0$ ( which is obvious )