Prove simple inequality probably with exponentials I can't prove
$$\frac{1+nx^2}{(1+x^2)^n} \leq 1$$
for $x,n>0
$
I know this is an easy question, but no matter how many exponential inequalities I try to use I can't crack it. Is there some sort of trick?

The trick is not to use exponential inequalities. Instead, use the binomial expansion :
$$(a+b)^n = \sum_{i=0}^{n} \binom{i}{n} a^ib^{n-i}$$
With $a=1$ and $b=x^2$, you get
$$(1+x^2)^n = 1 + n x^2 + \underbrace{\sum_{i=2}^{n} \binom{i}{n} (x^2)^{n-i}}_{\geqslant 0}$$
Hence, $(1+x^2)^n\geqslant 1 + n x^2$.
