How to verify the following function is convex or not? Consider function
$$f(x)=\frac{x^{n_{1}}}{1-x}+\frac{(1-x)^{n_{2}}}{x},x\in(0,1)$$
where $n_{1}$ and $n_2$ are some fixed positive integers.
My question: Is $f(x)$ convex for any fixed $n_1$ and $n_2$?
The second derivation of function $f$ is very complex, so I wish there exists other method to verify convex property.

In mathematics, a real-valued function  defined on an interval is called convex (or convex downward or concave upward) if the graph of the function lies below the line segment joining any two points of the graph. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. More generally, this definition of convex functions makes sense for functions defined on a convex subset of any vector space.according to wikipedia
A real valued function f : X → R defined on a convex set X in a vector space is called convex if, for any two points  x1,x2   in X and any  t belongs [0 1] we have
$f(t*x1+(1-t)*x2)&lt=(t*f(x1)+(1-t)f(x2))$ now let's take $n1$ and $n2$ some fixed values,let say 5 and 10,and try it
