# Answer

Lets simplify the equation a little bit:

\begin{eqnarray*}
a &=& b + \frac{c}{d} \
d(a) &=& d\left(b + \frac{c}{d}\right) \
ad &=& bd + c
\end{eqnarray*}

You cannot simply choose what part to multiply $d$ by. You have to multiply the whole thing.

For further proof plug in your equation into wolfram alpha and it will simplify it for you.