Example 1
Completion requirements
| Example 1 |
Simplify the expression \(\frac{256ab^2c}{4a^2bc}\). Identify the
non-permissible values.
Step 1: Factor the numerator and denominator.
Step 2: Determine the NPVs.
\(\begin{align}
a &\ne 0 \\
b &\ne 0 \\
c &\ne 0 \\
\end{align}\)
Step 3: Simplify by removing factors found in both the numerator and denominator.
Notice that two of the NPVs disappear in the simplified denominator. This is why NPVs must be identified before simplifying.
The simplified expression is \(\frac{64b}{a}, \thinspace a \ne 0,\thinspace b \ne 0,\thinspace c \ne 0\).
\[\frac{{256ab^2 c}}{{4a^2 bc}} = \frac{{2^8 ab^2 c}}{{2^2 a^2 bc}}\]
Step 2: Determine the NPVs.
\(\begin{align}
a &\ne 0 \\
b &\ne 0 \\
c &\ne 0 \\
\end{align}\)
Step 3: Simplify by removing factors found in both the numerator and denominator.
\[\frac{2^8ab^2c}{2^2a^2bc} =
\frac{2^6b}{a} = \frac{64b}{a}\]
\frac{2^6b}{a} = \frac{64b}{a}\]
Notice that two of the NPVs disappear in the simplified denominator. This is why NPVs must be identified before simplifying.
The simplified expression is \(\frac{64b}{a}, \thinspace a \ne 0,\thinspace b \ne 0,\thinspace c \ne 0\).