Question

Solve : ${lim}_{x\to 1}\frac{(2x-3)(\sqrt{x}-1)}{3x^2+3x-6}$

Answer 1

Let $L=\underset{x\to 1}{lim}\frac{(2x-3)(\sqrt{x}-1)}{3(x^2+x-1)}=\underset{x\to 1}{lim}\frac{(2x-3)(x-1)}{3(x+1)(x+2)(x-1)}L=\underset{x\to 1}{lim}\frac{2x-3}{3(x+1)(x+2)}=\frac{-1}{3\times 2\times 3}=\frac{-1}{18}$