Simplifying:
[tex]\begin{gathered} =\frac{(3-4i)(3\text{ - 4i) + (3+ 4i)(3 + 4i)}}{(3\text{ + 4i)(3 - 4i)}} \\ =\frac{3(3\text{ - 4i)-4i(3 - 4i)}+\text{ \lbrack}3(3\text{ + 4i)+4i(3 + 4i)\rbrack}}{(3\text{ + 4i)(3 - 4i)}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\frac{9-12i-12i+16i^2+\text{ \lbrack}9+12i+12i+16i^2\text{\rbrack}}{(3\text{ + 4i)(3 - 4i)}} \\ =\text{ }\frac{9-12i-12i+16i^2+\text{ \lbrack}9+12i+12i+16i^2\text{\rbrack}}{3\text{ (3 - 4i)+ 4i (3 - 4i)}} \\ =\text{ }\frac{9-12i-12i+16i^2+\text{ \lbrack}9+12i+12i+16i^2\text{\rbrack}}{9\text{ - 12i+12i - 1}6i^2} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\frac{9-24i+16i^2+\text{ }9+24i+16i^2}{9\text{ - 12i+12i - 1}6i^2} \\ =\text{ }\frac{9-24i+24i+\text{ }9+16i^2+16i^2}{9\text{ - 12i+12i - 1}6i^2} \\ =\text{ }\frac{9+\text{ }9+16i^2+16i^2}{9\text{ - 1}6i^2} \\ =\text{ }\frac{18+32i^2}{9\text{ - 1}6i^2} \end{gathered}[/tex][tex]\begin{gathered} \operatorname{Re}c\text{ all in complex number:} \\ i^2\text{ = -1} \\ We\text{ }would\text{ }replace\text{ }i^2\text{ with - 1 in the result above:} \\ =\text{ }\frac{18+32i^2}{9\text{ - 1}6i^2}=\text{ }\frac{18+32(-1)}{9\text{ - 1}6(-1)} \\ =\text{ }\frac{18-32}{9\text{+1}6} \end{gathered}[/tex][tex]=\frac{-14}{25}\text{ (option C)}[/tex]