A limit problem where $x\to 0$ I can't figure out how to compute this limit: $$\lim_{x\to 0}\dfrac{e^{3x^2}-e^{-3x^2}}{e^{x^2}-e^{-x^2}}$$ Any advice?

$$\lim_{x\to 0}\dfrac{e^{3x^2}-e^{-3x^2}}{e^{x^2}-e^{-x^2}}$$
$$=\lim_{x\to 0}\dfrac{e^{3x^2}-1-\left(e^{-3x^2}-1\right)}{e^{x^2}-1-\left(e^{-x^2}-1\right)}$$
$$=\dfrac{3\cdot\lim_{x\to 0}\dfrac{e^{3x^2}-1}{3x^2}-\left(\lim_{x\to 0}\dfrac{e^{-3x^2}-1}{-3x^2}\right)(-3)}{\lim_{x\to 0}\dfrac{e^{x^2}-1}{x^2}-\left(\lim_{x\to 0}\dfrac{e^{-x^2}-1}{-x^2}\right)(-1)}$$
Now use $\lim_{h\to0}\dfrac{e^h-1}h=1$
