Complex function defined on the real axis by a power series

Question

$f(z) = u(x,y)+iv(x,y)$ in the segment : $ y=0, 3.2\leq x \leq 3.8 $ is: $$ u(x,0)=\sum_{n=1}^{\infty}\Bigl({x\over4}\Bigr)^n+\sum_{n=0}^\infty \Bigl({3\over x}\Bigr)^n, v(x,0)=0 $$ Find $f(z)$ in the point $ z=5+i8$.$$$$ The power series is well defined for $ 3<x<4 $. I can rewrite $ u $ as: $$ u(x,0)= {x\over4-x}+{x \over x-3}$$ And this function is well defined for $ x\neq3, x\neq4$ (but is it equal to the power series outside of it's region of convergence?). Now I can maybe solve 2 Laplace's equations one for $u$ and one for $v$ with the initial condition $ u(x,0)= {x\over4-x}+{x \over x-3}$ and $v(x,0)=0$ with $-\infty<x<\infty $,and then maybe impose the CR conditions, but don't know how to really do it.