Can you please check if i solved this limit correctly?
$\lim_{x \to 1} \frac{\sin{(1-x)}}{\sqrt{x}-1} $
To skip writing of code , I'll just explain what i did .. First, I multiplied the expression by $\frac{\sqrt{x}+1}{\sqrt{x}+1}$. Then i got $\frac{\sin{(1-x)} * (\sqrt{x}+1)}{x-1}$. Next i pulled out the minus in from of the brackets in denumerator so i got: $\frac{\sin{(1-x)} * (\sqrt{x}+1)}{-(1-x)}$. Since $\frac{\sin{(1-x)}}{1-x}$ is equal to 1, I am left with $ -(\sqrt{x}+1)$. After exchanging x with 1 i get -2 as a result. Did i do this correctly?