calculus - Find this limit without using L'Hospital's rule

I have to find this limit without using l'Hôspital's rule:

$$\lim_{x\to 0} \frac{\alpha \sin \beta x - \beta \sin \alpha x}{x^2 \sin \alpha x}$$

Using L'Hôspital's rule gives:

$$\frac{\beta}{6(\alpha^2 - \beta^2)}$$
I am stuck where to begin without using the rule.