Example 3
Completion requirements
| Example 3 |
Simplify the expression \(\frac{2}{{m + 3}} + \frac{4}{{3\left( {m + 3} \right)}}\). Identify any non-permissible values.
Step 1: Identify the NPVs.
\(\begin{align}
m + 3 &\ne 0 \\
m &\ne -3 \\
\end{align}\)
Step 2: Determine the LCD.
The LCD is \(3\left( {m + 3} \right)\).
Step 3: Use the LCD to rewrite each term as an equivalent rational expression with the same denominator, and simplify.
\(\begin{align}
m + 3 &\ne 0 \\
m &\ne -3 \\
\end{align}\)
Step 2: Determine the LCD.
The LCD is \(3\left( {m + 3} \right)\).
Step 3: Use the LCD to rewrite each term as an equivalent rational expression with the same denominator, and simplify.
\[\begin{align}
\frac{{2\left( {\color{red}3} \right)}}{{\left( {m + 3} \right)\left( {\color{red}3} \right)}} + \frac{4}{{3\left( {m + 3} \right)}} &= \frac{6}{{3\left( {m + 3} \right)}} + \frac{4}{{3\left( {m + 3} \right)}} \\
&= \frac{{6 + 4}}{{3\left( {m + 3} \right)}} \\
&= \frac{{10}}{{3\left( {m + 3} \right)}}, \thinspace m \ne - 3 \\
\end{align}\]
\frac{{2\left( {\color{red}3} \right)}}{{\left( {m + 3} \right)\left( {\color{red}3} \right)}} + \frac{4}{{3\left( {m + 3} \right)}} &= \frac{6}{{3\left( {m + 3} \right)}} + \frac{4}{{3\left( {m + 3} \right)}} \\
&= \frac{{6 + 4}}{{3\left( {m + 3} \right)}} \\
&= \frac{{10}}{{3\left( {m + 3} \right)}}, \thinspace m \ne - 3 \\
\end{align}\]