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**1. Homework Statement**

Let ##x\in \mathbb{R} ##

Prove the conditional statement that,

if ## x>-1## then ## x^2 + \frac {1}{x^2+1} \geq 1##

**2. The attempt at a solution**

Suppose ## x>-1## is true.

Then ## x^2>1##

Then ## \frac{1}{2}>\frac {1}{x^2+1}##

Then ##x^2+ \frac{1}{2}>x^2+\frac {1}{x^2+1}##

After that I have no clue how to get to the part where ## x^2 + \frac {1}{x^2+1} \geq 1## happens. Pls help...