Question

lim x→0 $\lim_{x \to \0} 0 ( \sqrt{3-2x}- \sqrt{6x+3})/(x^2-x)$

Answer 1

$\lim_{x \to 0} \frac{ \sqrt{3-2x} - \sqrt{6x+3} }{x^2-x}= \lim_{x \to 0} \frac{3-2x-6x-3}{x(x-1)( \sqrt{3-2x}+ \sqrt{6x+3} )}= \lim_{x \to 0} \frac{-8}{(x-1)( \sqrt{3-2x}+ \sqrt{6x+3})} =\frac{4}{\sqrt{3}}$