Answer :
[tex]\begin{gathered} \frac{6-i}{5+4i} \\ \\ \text{Multiply by the conjugate} \\ \frac{6-i}{5+4i}\cdot\frac{5-4i}{5-4i} \\ \frac{30-24i-5i+4i^2}{25-20i+20i-16i^2} \\ \frac{30-29i+4i^2}{25-16i^2} \\ \\ \frac{30-29i+4(-1)}{25-16(-1)} \\ \\ \frac{30-4-29i}{25+16}=\frac{26-29i}{41} \end{gathered}[/tex]