The limit of a product is equal to the product of limits:
[tex]\displaystyle\lim_{x\to0}\frac{\sin x}{x^2-x}=\left(\lim_{x\to0}\frac{\sin x}x\right)\left(\lim_{x\to0}\frac1{x-1}\right)[/tex]
You should recognize the first limit, which has a value of 1. In the second limit, the expression [tex]\dfrac1{x-1}[/tex] is continuous at [tex]x=0[/tex], so its value is -1, and so the overall limit has a value of 1*(-1) = -1.
