I was learning (practicing to solve) simplifying the rational expressions. I know how to simplify the rational expressions... but I can't understand some part of the questions.
The question that I can't understand
If you look at this image, you could see sentence "First, let's set the denominator equal to zero and solve for n:", and there is "Select all that apply." too.
But, there was no any explanations about it must be denominator = 0. I found it just in hint, not a basic question..
So... why solving equation and suppose that denominator = 0 are related to simplifying the rational expressions?
And why we suppose denominator = 0 and we don't touch numerator..?
Is there any mathematical relationships between them?
I hope you (expert) will answer to my question, thanks.
The problem is that division by $0$ is undefined. Thus, before we begin simplifying an expression, we want to know when it is undefined. Remember that $0$ divided by something else is just $0$, so we don't need to worry about the numerator.
For example, the expression $\frac{1+x}{x}$ is undefined at $x=0$, but when $x=-1$, we just get $\frac{0}{-1}=0$.
As another example, consider $\frac{x}{x}$. Clearly this is just equal to $1$. However, the fraction is still undefined at $x=0$. That is because $\frac{0}{0}$ is undefined. To compensate, we can write that $\frac{x}{x}$ is equal to $1$ when $x\neq 0$.