Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2 - Page 69: 5

$\lim\limits_{x \to 3} \frac{x^2 - 2x}{x+1} = \frac 34$

Let us find the limit $\lim\limits_{x \to 3} \frac{x^2 - 2x}{x+1}$. The denominator of our function does not vanish at the point $ x = 3 $. Thus, we can substitute $x=3$ in our function in order to get the limit: $$ \lim\limits_{x \to 3} \frac{x^2 - 2x}{x+1} = \frac{3^2 - 2\cdot 3}{3+1} = \frac 34 $$