Example 2
Completion requirements
| Example 2 |
Simplify the rational expression \(\frac{{3x}}{{5x^2y}} \cdot \frac{{2y}}{{6x}}\). Identify any non-permissible values.
Step 1: Identify the NPVs.
Step 2: Simplify the expression.
\(\begin{align}
\frac{{3x}}{{5x^2 y}} \cdot \frac{{2y}}{{6x}} &= \frac{{6xy}}{{30x^3 y}} \\
&= \frac{1}{{5x^2 }},\thinspace x \ne 0,\thinspace y \ne 0 \\
\end{align}\)
\(\begin{align}
x^2 &\ne 0 \\
x &\ne 0 \\
\end{align}\)
x^2 &\ne 0 \\
x &\ne 0 \\
\end{align}\)
\(y \ne 0\)
Step 2: Simplify the expression.
\(\begin{align}
\frac{{3x}}{{5x^2 y}} \cdot \frac{{2y}}{{6x}} &= \frac{{6xy}}{{30x^3 y}} \\
&= \frac{1}{{5x^2 }},\thinspace x \ne 0,\thinspace y \ne 0 \\
\end{align}\)