How to solve Recurrence relation: $T(n) = T(n/3) + T(n/5) + n$ Given the following: $T(n) = T(n/3) + T(n/5) + n$
The aim is to find the upper bound of this solution. 
I have tried to solve this using Master's Theorem, but this does not apply for this problem.
My next best options would be Substitution or Iteration, but I am having troubles finding examples similar enough to follow these methods to solve this relation.
If I were to make a "guess" to use for substitution method I would use $T(n) \leq cn$ but after working through the problem I am unable to reach any sort of a solution

Let's check if 
\begin{equation}
 T(n) = \frac{15}{7}n
\end{equation}
is a solution for our recursion. 
\begin{align}
 T(n) &= \frac{15}{7}n \\
 T(\frac{n}{3}) &=\frac{1}{3} \frac{15}{7}n\\
 T(\frac{n}{5}) &=\frac{1}{5} \frac{15}{7}n
\end{align}
So
\begin{equation}
 T(\frac{n}{3}) + T(\frac{n}{5}) + n 
 =
 \frac{1}{3} \frac{15}{7}n +
 \frac{1}{5} \frac{15}{7}n
 +
 n 
\end{equation}
which is 
\begin{equation}
 T(\frac{n}{3}) + T(\frac{n}{5}) + n 
 =
 \frac{3}{7}n + \frac{5}{7}n + n
 =
 \frac{8+7}{7}n
 =
 \frac{15}{7}n
 =
 T(n)
\end{equation}
So
\begin{equation}
 T(n) = \frac{15}{7}n
\end{equation}
is indeed a solution.
