How can I simplify this rational expression? I am trying to simplify $$ \frac{3(5^{k+1} - 1) + 4(3 \;\cdot\;5^{k+1})}{4}$$ to get to $$\frac{3(5^{k+2}-1)}{4} $$
I start with $$ \frac{3(5^{k+1} - 1) + 12\;\cdot\;5^{k+1}}{4}$$
$$= \frac{3\;\cdot\;5^{k+1} - 3 + 12\;\cdot\;5^{k+1}}{4} $$
then I am stuck. 

$$\begin{align}
& \frac{3(5^{k+1} - 1) + 4(3 \;\cdot\;5^{k+1})}{4}\\
= & \frac{3(5^{k+1} - 1) + 3(4 \;\cdot\;5^{k+1})}{4}\\
= & \frac{3(1\cdot5^{k+1} + 4 \;\cdot\;5^{k+1} - 1)}{4}\\
= & \frac{3(5\cdot5^{k+1} - 1)}{4}\\
= & \frac{3(5^{k+2} - 1)}{4}
\end{align}$$
