Expand $[2e^{rx^2}-e^{mx^2-\sigma x} -e^{mx^2+\sigma x}]/[{e^{mx^2+\sigma x}-e^{mx^2-\sigma x}}]$ around $x=0$ and simplify (second order expansion)
I'm a bit stumped here. I get something like $2+2rx^2+o(x^2)-1-mx^2+\sigma x - o(x^2) - mx^2 - \sigma x - o(x^2)$ for the numerator -- am I on the right track?