The given fraction is
[tex]\frac{7+i}{3-i}[/tex]
We will multiply up and down by the conjugate of down (3 + i)
[tex]\begin{gathered} \frac{7+i}{3-i}\times\frac{3+i}{3+i}= \\ \\ \frac{(7+i)(3+i)}{(3-i)(3+i)}= \\ \\ \frac{(7)(3)+(7)(i)+(i)(3)+(i)(i)}{(3)(3)-(i)(i)}= \end{gathered}[/tex]
Add the like terms
[tex]\begin{gathered} \frac{21+7i+3i+i^2}{9-i^2}= \\ \\ \frac{21+10i-1}{9-(-1)}= \\ \\ \frac{20+10i}{9+1}= \\ \\ \frac{20+10i}{10} \end{gathered}[/tex]
Take 10 as a common factor from up
[tex]\begin{gathered} \frac{10(2+i)}{10}= \\ \\ 2+i \end{gathered}[/tex]
The answer is C
