Example 1
Completion requirements
| Example 1 |
Simplify the expression \(\frac{{3x}}{{4\left( {x - 3} \right)}} - \frac{{2x}}{{x - 3}} \cdot \frac{5}{{4x}}\). Identify any non-permissible values.
Step 1: Identify the NVPs.
Step 2: Determine which operation to perform first, and simplify.
According to BEDMAS, multiplication comes before subtraction.
Step 3: Determine the next operation to be performed, and simplify.
The next operation (and last one) is subtraction.
\(\begin{align}
x - 3 &\ne 0 \\
x &\ne 3 \\
\end{align}\)
x - 3 &\ne 0 \\
x &\ne 3 \\
\end{align}\)
\(x \ne 0\)
Step 2: Determine which operation to perform first, and simplify.
According to BEDMAS, multiplication comes before subtraction.
\[\begin{align}
{\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{2x}{x - 3} \cdot \frac{5}{4x} &= {\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{10x}{4x\left( {x - 3} \right)} \\
&= {\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{5}{2\left( {x - 3} \right)}
\end{align}\]
{\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{2x}{x - 3} \cdot \frac{5}{4x} &= {\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{10x}{4x\left( {x - 3} \right)} \\
&= {\color{red}\frac{3x}{4\left( {x - 3} \right)}} - \frac{5}{2\left( {x - 3} \right)}
\end{align}\]
Step 3: Determine the next operation to be performed, and simplify.
The next operation (and last one) is subtraction.
\[\begin{align}
\frac{3x}{4\left( {x - 3} \right)} - \frac{5\left({\color{red}2}\right)}{\left[ {2\left( {x - 3} \right)} \right]\left( {\color{red}2}\right)} &= \frac{3x}{4\left( {x - 3} \right)} - \frac{10}{4\left( {x - 3} \right)} \\
&= \frac{3x - 10}{4\left( {x - 3} \right)} ,\thinspace x \ne 0,\thinspace 3 \end{align}\]
\frac{3x}{4\left( {x - 3} \right)} - \frac{5\left({\color{red}2}\right)}{\left[ {2\left( {x - 3} \right)} \right]\left( {\color{red}2}\right)} &= \frac{3x}{4\left( {x - 3} \right)} - \frac{10}{4\left( {x - 3} \right)} \\
&= \frac{3x - 10}{4\left( {x - 3} \right)} ,\thinspace x \ne 0,\thinspace 3 \end{align}\]