find the points at which the following function is undefined, then find the limit at these points. $$f(x) = \frac{x^2 + 3x + 2}{x + 2}$$
The point at which the function is undefined is $x = -2$, then I factorized the numerator, deleted $(x+2)$ from numerator and denominator then the limit equals -1. am I right?
But why did not we factorize from the beginning then we obtain $$f(x) = x+1$$
and the function now is defined for all $x \in \mathbb{R}$?
If you factorised in the beginning and cancelled out the factor $(x+2)$, you cancelled $0$ from a $0$ in a division, when $x$ was equal to $-2$, which is not a valid operation.
For example $$1 \times 0= 2 \times 0$ and cancelling out $0$ both the sides, we have $1=2$.