I am trying to solve a worksheet that has questions related to Rational Expressions and one of the questions in that worksheet asks us to simplify and find the excluded value of a rational expression. I got to solve a question that was:- Rational Expression
As I Simplified I the above rational Expression I got:- Simplified Expression
Now I know that if want to find the excluded value than I need to make the denominator equal to zero and I would get the excluded value that is {0, -5} without simplifying but I would like to know that if I do simplify than is there any way that I can get the excluded value from the simplified expression.
Thanks
Hint: You can factor out $\frac23$ in the numerator.
$$\frac{\frac23\cdot (3a^2+15a)}{3a^2+15a}=\frac23 \ \ \forall a \in \mathbb R \backslash \{0, -5\}$$