Answer
(a)
According to the distributive property of addition,
$a\left( b+c \right)=ab+ac$
Use the above property in the given formula,
$\begin{align}
& \frac{D\left( A+1 \right)}{24}=\frac{D\cdot A+D\cdot 1}{24} \\
& =\frac{DA+D}{24}
\end{align}$
Both formulae are same as shown above.
(b)
Substitute $200$ for $D$ and $12$ for $A$ in the first formula.
$\begin{align}
& \frac{D\left( A+1 \right)}{24}=\frac{200\left( 12+1 \right)}{24} \\
& =\frac{200\left( 13 \right)}{24} \\
& =108.33 \\
& \approx 108
\end{align}$
Substitute $200$ for $D$ and $12$ for $A$ in the second formula.
$\begin{align}
& \frac{DA+D}{24}=\frac{200\cdot 12+200}{24} \\
& =\frac{2400+200}{24} \\
& =108.33 \\
& \approx 108
\end{align}$
With both expressions, the proper dose is approximately$108\,\text{mg}$.
It is easier to use the first formula as an additional step of addition is reduced.
