(4+3i)/(4-6i) - (5+3i)/(2+3i) =
= (4+3i) / (4-6i) * [(4+6i) / (4+6i)] - (5+3i) / (2+3i) * [(2-3i) / (2-3i)] =
= [(4+3i)(4+6i) / (4-6i)(4+6i)] - [(5+3i)(2-3i) / (2+3i)(2-3i)] =
= (16+12i+24i-18)/(16+36) - (10+6i-15i+9)/(4+9) =
= (-2+36i)/52 - (19-9i)/13 =
= (-2+36i)/52 - (19-9i)/13 * (4/4) =
= (-2+36i)/52 - 4*(19-9i)/52 =
= (-2+36i - 76+36i) / 52 =
= (-78+72i) / 52 =
= 3*(-13+12i) / 26