Example 3
Completion requirements
| Example 3 |
Determine the non-permissible values for the expression \(\frac{6}{{9x^2 - 25y^2}}\).
Step 1: Factor the denominator.
\(\frac{6}{{9x^2 - 25y^2 }} = \frac{6}{{\left( {3x - 5y} \right)\left( {3x + 5y} \right)}}\)
Step 2: Determine the values of the variables that cause the denominator to equal zero.
The NPVs for \(x\) are \(\pm \frac{5}{3}y\). The expression can be rewritten as \(\frac{6}{{9x^2 - 25y^2}},\thinspace x \ne \pm \frac{5}{3}y\).
Alternatively, the NPVs could be stated in the form \(y \ne \pm \left (\frac{3}{5} \right ) x\).
\(\frac{6}{{9x^2 - 25y^2 }} = \frac{6}{{\left( {3x - 5y} \right)\left( {3x + 5y} \right)}}\)
Step 2: Determine the values of the variables that cause the denominator to equal zero.
\(\begin{align}
3x - 5y &\ne 0 \\
x &\ne \frac{5}{3}y \\
\end{align}\)
3x - 5y &\ne 0 \\
x &\ne \frac{5}{3}y \\
\end{align}\)
\(\begin{align}
3x + 5y &\ne 0 \\
x &\ne - \frac{5}{3}y \\
\end{align}\)
3x + 5y &\ne 0 \\
x &\ne - \frac{5}{3}y \\
\end{align}\)
Alternatively, the NPVs could be stated in the form \(y \ne \pm \left (\frac{3}{5} \right ) x\).
| For further information about non-permissible values, see p. 312 of Pre-Calculus 11. |