Example 2
Completion requirements
| Example 2 |
Determine the non-permissible values for the expression \(\frac{5}{3x^2 - 6x}\).
Step 1: Factor the denominator.
In this example, in order to determine the NPVs, you must factor the denominator.
Step 2: Determine the values of \(x\) that cause the denominator to equal zero.
The NPVs are \(0\) and \(2\). This expression is written as \(\frac{5}{{3x^2 - 6x}}, \thinspace x \ne 0, \thinspace 2\).
In this example, in order to determine the NPVs, you must factor the denominator.
\[\frac{5}{{3x^2 - 6x}} = \frac{5}{{3x\left( {x - 2} \right)}}\]
Step 2: Determine the values of \(x\) that cause the denominator to equal zero.
\(\begin{align}
3x &\ne 0 \\
x &\ne 0 \\
\end{align}\)
3x &\ne 0 \\
x &\ne 0 \\
\end{align}\)
\(\begin{align}
x - 2 &\ne 0 \\
x &\ne 2 \\
\end{align}\)
x - 2 &\ne 0 \\
x &\ne 2 \\
\end{align}\)