Solve the limit as $x$ approaches $1$.
$$\lim_{x\rightarrow 1} \frac{\sin |x-1|}{x-1} $$
I know that $x$ approaches $1$ from negative side and positive side but I don't know where to start it. I tried to cancel out the $x-1$ on the bottom but did not work.
Thanks.

Hint: for $x<1, |x-1| = -(x-1)$ and for $x > 1, |x-1| = (x-1)$.
Also $\lim_{y \to 0} \frac{\sin y}{y} = 1$ 
What happens when one-sided limits are different?
