Question

Find all numbers for which the rational expression is undefined. (4v^2)/(8v+9)

Answer 1

A rational expression is undefined when the denominator is equal to zero. For the expression \(\frac{4v^2}{8v + 9}\), we need to find the values of \(v\) that make the denominator \(8v + 9\) equal to zero.

To find these values, we set the denominator equal to zero and solve for \(v\):

\[
8v + 9 = 0
\]

Subtract \(9\) from both sides:

\[
8v = -9
\]

Now, divide both sides by \(8\):

\[
v = -\frac{9}{8}
\]

Thus, the expression \(\frac{4v^2}{8v + 9}\) is undefined when \(v = -\frac{9}{8}\).