Question

For what value of the variable is the expression undefined?
5/c^2+6c

Answer 1

\[5 \over c^2+6c\]

Answer 2

if c^2+6c=0 the expression will be undefined

Answer 3

In a rational expression, the 'danger zone' is usually the denominator:
\( \large \frac{P(x)}{\color{red}{Q(x)}} \)
If \(Q(c) = 0\), then \(c\) would cause the denominator to be 0. Division by 0 is considered undefined (for our purposes). So, that \(c\) value is our interest.
\( \large \frac{5}{\color{red}{c^2 + 6c}} \)
Similar to the general example; if \(c^2 + 6c = 0\), then \(c\) will cause the denominator to be 0.