Solving simple equation I can't seem to solve/simplify step by step to get from equation 3) to 4) as they do in this paper. As per the paper:

3) $p = \frac{p' + (r-R)p}{1+r}$
Because both sides of equation 3) involve the current price, $p$, the equation can be solved as follows:
4) $p = \frac{p'}{1+R}$

Could somebody please step by step show how I'd solve this step please? 

We start with the original equation:
\begin{align*}
p = \frac{p' + (r-R)p}{1+r}
\end{align*}
We want to obtain $p$ as a function of the other values. So, we first want to collect all terms with $p$ on the same side. We do this by splitting the fraction and bringing one term over.
\begin{align*}
p &= \frac{p'}{1+r} + \frac{(r-R)p}{1+r} \\
p - \frac{(r-R)p}{1+r} &= \frac{p'}{1+r}
\end{align*}
Now, we can factor out the $p$ on the left side, and put everything on the same denominator.
\begin{align*}
p \left(
1 - \frac{(r-R)}{1+r}
\right) &= \frac{p'}{1+r} \\
p \left(
\frac{1+r}{1+r} - \frac{r-R}{1+r}
\right) &= \frac{p'}{1+r} \\
p \left(
\frac{1+R}{1+r}
\right) &= \frac{p'}{1+r}
\end{align*}
(Note of course that $(1+r)-(r-R) = (1+r) + (-r +R) = 1+R$.). Finally, we multiply both sides of the equation by $(1+r)/(1+R)$ to get:
\begin{align*}
p \left( \frac{1+R}{1+r} \right) \cdot \frac{1+r}{1+R}
&= \frac{p'}{1+r} \cdot \frac{1+r}{1+R} \\
p = \frac{p'}{1+R}
\end{align*}
And this is the desired result.
