Solution:

$h(n)=\left(\frac{1}{2}\right)^n u(n) ; x(n)=\left(\frac{3}{4}\right)^n u(n)\\ $

$\begin{aligned} H\left(e^{j \omega}\right)= & \frac{1}{1-\frac{1}{2} e^{-j \omega}} \quad ; \quad X\left(e^{j \omega}\right)=\frac{1}{1-\frac{3}{4} e^{-j \omega}} \\\\ & Y\left(e^{j \omega}\right)=H\left(e^{j \omega}\right) X\left(e^{j \omega}\right)\\ \end{aligned}$

$ \begin{aligned} & Y\left(e^{j \omega}\right)=\frac{1}{1-\frac{1}{2} e^{-j \omega}} \cdot \frac{1}{1-\frac{3}{4} e^{-j \omega}}=\frac{e^{j \omega}}{e^{j \omega}-\frac{1}{2}} \cdot \frac{e^{j \omega}}{e^{j \omega}-\frac{3}{4}} \\\\ …