Find $\displaystyle \lim_{x\rightarrow1} \frac{sin(x-1)}{x^2+x-2}$

$\displaystyle = \lim_{x\rightarrow1}\frac{sin(x-1)}{(x+2)(x-1)}$

do the $\displaystyle (x-1)$ terms cancel out? If so, doesn't that leave me with $\displaystyle \lim_{x\rightarrow1}\frac{sinx}{x+2}$ ?

then by direct sub $\displaystyle \lim_{x\rightarrow1}\frac{sinx}{x+2} = \frac{sin1}{3}$ ?