Answer:
7-4i
Step-by-step explanation:
Multiplying the numerator and denominator by $1-2i$ gives
\begin{align*}
\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\
&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\
&= \frac{5(3 + 2i)(1 - 2i)}{5} \\
&= (3 + 2i)(1 - 2i) \\
&= 3 + 2i - 6i - 4i^2 \\
&= 3 + 2i - 6i + 4 \\
&= \boxed{7 - 4i}.
