Example 1
Completion requirements
| Example 1 |
Verify that \(v = 3\) is an extraneous root for the rational equation \(\frac{{4v^2 - 11v - 3}}{{v^2 - 5v + 6}} = 13\).
To verify that \(v = 3\) is an extraneous root, substitute \(3\) for \(v\) in the equation, and show that the left side does not equal the right side.
| Left Side | Right Side |
|---|---|
|
\[\begin{array}{r}
\frac{{4v^2 - 11v - 3}}{{v^2 - 5v + 6}} \\ \frac{{4\left( 3 \right)^2 - 11\left( 3 \right) - 3}}{{\left( 3 \right)^2 - 5\left( 3 \right) + 6}} \\ \frac{{4\left( 9 \right) - 33 - 3}}{{9 - 15 + 6}} \\ \frac{{36 - 36}}{{15 - 15}} \\ \frac{0}{0} \\ {\rm{undefined}} \\ \end{array}\] |
\(13\) |
| LS \(\ne\) RS\(\hspace{30pt}\) | |