Question

lim\(\dfrac{2x-\sqrt{3x^2+2x}}{x^2-3x+2}\)(x-->2)

Answer 1

\(\lim\limits_{x\rightarrow2}\dfrac{2x-\sqrt{3x^2+2x}}{x^2-3x+2}=\lim\limits_{x\rightarrow2}\dfrac{\left(2x-\sqrt{3x^2+2x}\right)\left(2x+\sqrt{3x^2+2x}\right)}{\left(x-1\right)\left(x-2\right)\left(2x+\sqrt{3x^2+2x}\right)}\)

\(=\lim\limits_{x\rightarrow2}\dfrac{x^2-2x}{\left(x-1\right)\left(x-2\right)\left(2x+\sqrt{3x^2+2x}\right)}\)

\(\lim\limits_{x\rightarrow2}\dfrac{x}{\left(x-1\right)\left(2x+\sqrt{3x^2+2x}\right)}=\dfrac{2}{1\left(4+4\right)}=\dfrac{1}{4}\)