solving for values of x where a (simplified) expression is undefined

Question

I'm working through Algebra 2 on Khan Academy, and I've come across an example that simplifies $\frac{6x^3 + 2x^2}{10x^2}$ as $\frac{3x +1}{5}$ and then states that 'even in the simplified form, it is clear that $x = 0$ is the only value for which the expression is undefined'.

I'm a little lost on how this is evident in the simplified form, as I would have thought $x = 0$ would evaluate to $0.2$. Can anyone explain?

Answer 1

You have to be careful with the simplified expression since

$$\frac{6x^3+2x^2}{10x^2} = \frac{3x+1}{5}, \text{ for } x \neq 0.$$

This subtle restriction exists because in order to get to the simplified form, you need to divide the numerator and denominator by $5x^2$ and if $x = 0$, then $5x^2 = 0$ as well and then you'd be dividing by $0$.