$\lim_{x \to 1} {\frac{x^3-1}{x^2-1}}$
Is there a way to evaluate this limit when $x$ Approaches 1 without using a graph? From graph, its easy to see, that as its $\frac{3}{2}$ but how do we simplify and break the fraction down because if I substitute $x=1$ to the expression I get $\frac{0}{0}$
There are several tricks you can use. For cases where you get $\frac00$ you can use L'Hospital's rule to get
$$\lim_{x\to 1} \frac{x^3-1}{x^2-1} = \lim_{x\to 1} \frac{3x^2}{2x} = \frac32$$
In addition, as shown by @geetha290krm, you can sometimes factor the numerator and denominator to get something that isn't indeterminate.
